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Recent questions and answers in Probability
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GATE200551
Box $P$ has $2$ red balls and $3$ blue balls and box $Q$ has $3$ red balls and $1$ blue ball. A ball is selected as follows: (i) select a box (ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes $P$ ... that it came from the box $P$ is: $\dfrac{4}{19}$ $\dfrac{5}{19}$ $\dfrac{2}{9}$ $\dfrac{19}{30}$
answered
2 days
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in
Probability
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Shamim Ahmed
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135
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1.2k
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gate2005
probability
conditionalprobability
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1
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2
GATE ME 2018 Normal Distribution
Let X1, X2 be two independent normal random variables with means p1, p2 and standard deviations a1, a2 respectively. Consider Y =X1X2; µ1=µ2=1, σl=1, σ2=2. Then. (a) Y is normal distributed with mean 0 and variance 1 (b) Y is normally ... Y has mean 0 and variance 5, but is NOT normally distributed (d) Y has mean 0 and variance 1, but is NOT normally distributed
answered
6 days
ago
in
Probability
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Mk Utkarsh
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20.3k
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probability
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0
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3
UGC net July 2018 Q84
Digital data received from a sensor can fill up 0 to 32 buffers. Let the sample space be S={0, 1, 2, ………., 32} where the sample j denote that j of the buffers are full and p(i) = 1 / 566 *(33 – i). Let A denote the event that the even number of buffers are full. Then p(A) is: (A) 0.515 (B) 0.785 (C) 0.758 (D) 0.485
[closed]
asked
6 days
ago
in
Probability
by
Dimpu1211
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7
points)

12
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0
votes
1
answer
4
Probability  Gravner37
A factory has three machines, M1, M2, and M3, that produce items (say, light bulbs). It is impossible to tell which machine produced a particular item, but some are defective. Here are the known numbers: machine proportion of items made prob. any made item is ... 5 0.003 You pick an item, test it, and find it is defective. What is the probability that it was made by M2?
answered
Oct 13
in
Probability
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Paras Nath
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probability
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+5
votes
4
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5
CMI2012A07
A man has three cats. At least one is male. What is the probability that all three are male? $\frac{1}{2}$ $\frac{1}{7}$ $\frac{1}{8}$ $\frac{3}{8}$
answered
Oct 9
in
Probability
by
Pradeep A
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81
points)

300
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cmi2012
probability
+1
vote
1
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6
expected amount
Jessica is playing a game where there are 4 blue markers and 6 red markers in a box. She is going to pick 3 markers without replacement. If she picks all 3 red markers, she will win a total of $500. If the first marker she picks is red but not all 3 ... red, she will win a total of $100. Under any other outcome, she will win $0. What is the expected value of Jessica's winnings?
answered
Oct 7
in
Probability
by
Mk Utkarsh
Boss
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20.3k
points)

34
views
+1
vote
1
answer
7
Birthday Paradox
In a room of $23$ people what is the probability that $2$ of. them has a birthday in common?
answered
Oct 6
in
Probability
by
Raghav Khajuria
(
475
points)

93
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probability
birthday
+1
vote
0
answers
8
Probability of missing the bus
You arrive at bus stop some time uniformly distributed between $10:00$ and $10:15$ and bus leaves the bus stop sometime uniformly distributed between $10:00$ and $10:25$. What is the probability of you missing the bus?
asked
Oct 5
in
Probability
by
Mk Utkarsh
Boss
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20.3k
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61
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probability
uniformdistribution
+1
vote
0
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9
TestBook Probability
Consider the production of iron rods having diameter X which is normally distributed with mean 2 in. and standard deviation 0.008 in. Using $\phi$(0.25) = 0.99, where $\phi$ is the cumulative distribution function (c.d.f.) of a standard normal ... standard deviation 1, the percentage of defectives we can expect if we set the tolerance limits at 2 0.02 in is _______ .
asked
Oct 4
in
Probability
by
Mk Utkarsh
Boss
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20.3k
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40
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testbooktestseries
probability
0
votes
1
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10
Probability Gravner 79.a
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (a) Determine c.
answered
Oct 4
in
Probability
by
Mk Utkarsh
Boss
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20.3k
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18
views
gravner
probability
engineeringmathematics
randomvariable
0
votes
2
answers
11
Probability Gravner 76
Assume that $X$ is Normal with mean $\mu$ $=$ $2$ and variance $\sigma^2$ $=$ $25$. Compute the probability that $X$ is between $1$ and $4$.
answered
Oct 4
in
Probability
by
Mk Utkarsh
Boss
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20.3k
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25
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probability
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engineeringmathematics
randomvariable
normaldistribution
+11
votes
6
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12
TIFR2013A6
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise twothirds of the population the park and give a correct answer to requests for directions with probability $\dfrac{3}{4}$. The air of Kabrastan has an amnesaic quality, ... )$ $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{2}{3}\right)$ $\left(\dfrac{3}{4}\right)$
answered
Oct 4
in
Probability
by
Subarna Das
Boss
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11.5k
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526
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tifr2013
probability
0
votes
0
answers
13
InclusionExclusion
$N$ people toss their hat into a bin, randomly shuffled, returned one hat to each person. What is the probability that $5$th person got his own hat?
asked
Oct 4
in
Probability
by
srestha
Veteran
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98.8k
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61
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discretemathematics
probability
inclusionexclusion
0
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0
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14
Sheldon Ross Chapter 2.7
The chess clubs of two schools consists of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the ... schools but will not play each other? (c) exactly one of Rebecca and Elise will be chosen to represent her school?
asked
Oct 2
in
Probability
by
Abhijit Sen 4
(
299
points)

5
views
0
votes
1
answer
15
ugc net 2018 july80
answered
Oct 2
in
Probability
by
kmittal1908
(
35
points)

130
views
0
votes
1
answer
16
MADE EASY TEST SERIES QUESTION
answered
Oct 2
in
Probability
by
Mk Utkarsh
Boss
(
20.3k
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32
views
+15
votes
3
answers
17
GATE2006IT22
When a coin is tossed, the probability of getting a Head is $p, 0 < p < 1$. Let $N$ be the random variable denoting the number of tosses till the first Head appears, including the toss where the Head appears. Assuming that successive tosses are independent, the expected value of $N$ is $\dfrac{1}{p}$ $\dfrac{1}{(1  p)}$ $\dfrac{1}{p^{2}}$ $\dfrac{1}{(1  p^{2})}$
answered
Sep 29
in
Probability
by
Anup
(
29
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1.4k
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gate2006it
probability
binomialdistribution
expectation
normal
0
votes
0
answers
18
ME2018 Set 1 Probability
A six faced fair dice is rolled five times. what is the probability of obtaining "ONE" atleast 4 times?
asked
Sep 27
in
Probability
by
aditi19
Junior
(
863
points)

42
views
gate2018analysis
probability
0
votes
1
answer
19
Probability Gravner 78
How many times do you need to toss a fair coin to get $100$ heads with probability $90$%?
answered
Sep 27
in
Probability
by
aditi19
Junior
(
863
points)

14
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
0
answers
20
Probability Gravner 82.c
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (c) How large should $n$ be so that the probability in(b) is larger than $0.99$?
asked
Sep 27
in
Probability
by
Pooja Khatri
Active
(
4.3k
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22
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
0
answers
21
Probability Gravner 82.b
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (b) Write down an approximation, in terms on $n$ and $\phi$, of the probability that $M$ differs from its expectation by less than $10$ %
asked
Sep 27
in
Probability
by
Pooja Khatri
Active
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4.3k
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10
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
0
answers
22
Probability Gravner 82.a
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (a) Compute the expectation $EM$.
asked
Sep 27
in
Probability
by
Pooja Khatri
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4.3k
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16
views
gravner
probability
engineeringmathematics
randomvariable
0
votes
0
answers
23
Probability Gravner 81.b
Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads. (b) Approximately how many times do you need to play so that you win at least $250$ dollar with probability at least $0.99$.
asked
Sep 27
in
Probability
by
Pooja Khatri
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(
4.3k
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14
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
0
answers
24
Probability Gravner 81.a
Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads. (a) Assume that you play this game $300$ times. What is, approximately, the probability that you win at least $250$ dollar ?
asked
Sep 27
in
Probability
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Pooja Khatri
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4.3k
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10
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probability
gravner
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randomvariable
0
votes
0
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25
Probability Gravner 80.c
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval. (c) ... $M$ be the amount of time of the show that you miss because of th call. Compute the expected value of $M$.
asked
Sep 27
in
Probability
by
Pooja Khatri
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4.3k
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11
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
0
answers
26
Probability Gravner 80.b
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval (b) At $8.30$, the call still hasn't arrived. What is the probability that it arrives in the next $10$ minutes?
asked
Sep 27
in
Probability
by
Pooja Khatri
Active
(
4.3k
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5
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
0
answers
27
Probability Gravner 80
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval. (a) Compute the probability that the call arrives between $8.30$ and $8.20$.
asked
Sep 27
in
Probability
by
Pooja Khatri
Active
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4.3k
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6
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
0
answers
28
GATE 200724, https://gateoverflow.in/1222/gate200724
asked
Sep 27
in
Probability
by
sakharam
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2.3k
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42
views
probability
0
votes
1
answer
29
Probability Gravner 75.c
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 3 $\sigma$ ?
answered
Sep 27
in
Probability
by
Balaji Jegan
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2.3k
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10
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probability
gravner
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randomvariable
0
votes
1
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30
Probability Gravner 75.b
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 2 $\sigma$ ?
answered
Sep 27
in
Probability
by
Balaji Jegan
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2.3k
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8
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probability
gravner
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0
votes
0
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31
Probability Gravner 79.c
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (c) Determine the probability density function of $Y$ $=$ $X^2$
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Sep 26
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Probability
by
Pooja Khatri
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4.3k
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9
views
probability
gravner
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randomvariable
0
votes
0
answers
32
Probability Gravner 79.b
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (b) Compute $\text{E(1/X)}$.
asked
Sep 26
in
Probability
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Pooja Khatri
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4.3k
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6
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probability
gravner
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randomvariable
0
votes
0
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33
Probability Gravner 77
A roulette wheel has $38$ slots: $18$ red, $18$ red, $2$ green. The ball ends at one of these at random. You are a player who plays a large number of games and makes an even bet of $1$ dollar on red in every game. After $n$ games, what is the probability that you are ahead? Answer this for $n=100$ and $n= 1000$.
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Sep 26
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Probability
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Pooja Khatri
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4.3k
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4
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probability
gravner
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randomvariable
0
votes
0
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34
Probability Gravner 75.a
What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
(
4.3k
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5
views
gravner
probability
engineeringmathematics
randomvariable
+1
vote
0
answers
35
Probability  Gravner74
Let X be a $N(\mu , \sigma^2)$ random variable and let $Y = \alpha X+\beta$, with $\alpha$ > $0$. How is $Y$ distributed?
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
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4.3k
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10
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probability
gravner
engineeringmathematics
randomvariable
0
votes
0
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36
Probability  Gravner73
Assume that a light bulb lasts on average $100$ hours. Assuming exponential distribution, compute the probability that it lasts more than $200$ hours and the probability that it lasts less than $50$ hours.
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
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4.3k
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10
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gravner
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0
votes
0
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37
Probability  Gravner72
A uniform random number $X$ divides $[0,1]$ into two segments. Let $R$ be the ratio of the smaller versus the larger segment. Compute the density of $R$.
asked
Sep 26
in
Probability
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Pooja Khatri
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4.3k
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5
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probability
gravner
engineeringmathematics
randomvariable
0
votes
0
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38
Probability  Gravner71
Assume that X is uniform on [0,1]. What is $P(X\epsilon Q)$? What is the probability that the binary expansion of X starts with 0.010?
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Sep 26
in
Probability
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Pooja Khatri
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4.3k
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6
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probability
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0
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0
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39
Probability  Gravner70
Assume that X has density $fx(x) = \begin{Bmatrix} 3x^{2} &if(x\epsilon [0,1]), \\ 0& otherwise \end{Bmatrix}$ Compute the density fy of Y= 1X4
asked
Sep 26
in
Probability
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Pooja Khatri
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4.3k
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2
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0
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0
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40
Probability  Gravner69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (c) Determine EX and Var(X).
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Sep 26
in
Probability
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Pooja Khatri
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