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General
From last few days I am trying to solve Sheldon Ross problems. But not able to solve it. So those who have solved it kindly tell me how to strengthen the concepts as to solve the problems...........and also is the level of problems given in it are as per GATE requirement??
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TIFR2010A13
A cube whose faces are colored is split into $1000$ small cubes of equal size. The cubes thus obtained are mixed thoroughly. The probability that a cube drawn at random will have exactly two colored faces is: $0.096$ $0.12$ $0.104$ $0.24$ None of the above
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tifr2010
probability
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GATE200724
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these
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gate2007
probability
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4
GATE19942.8
Let $A, B$ and $C$ be independent events which occur with probabilities $0.8, 0.5$ and $0.3$ respectively. The probability of occurrence of at least one of the event is _____
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gate1994
probability
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Sheldon Ross Chapter 2
If it is assumed that all (52 5) poker hands are equally likely, what is the probability of being dealt (a) a ﬂush? (A hand is said to be a ﬂush if all 5 cards are of the same suit.) (b) one pair? (This occurs when the cards have denominations a, a, ... distinct.) (c) two pairs? (This occurs when the cards have denominations a, a, b, b, c, wherea, b, andc are all distinct.)
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Probability
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161
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3
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4
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GATE200827
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is $0.6$. If she studies mathematics on a day, then the probability that she studies computer ... science on Monday, what is the probability that she studies computer science on Wednesday? $0.24$ $0.36$ $0.4$ $0.6$
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gate2008
probability
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7
Sheldon Ross Chapter 2
If it is assumed that all (525) poker hands are equally likely, what is the probability of being dealt (a) a ﬂush? (A hand is said to be a ﬂush if all 5 cards are of the same suit.) (b) one pair? (This occurs when the cards have denominations a, a, b ... distinct.) (c) two pairs? (This occurs when the cards have denominations a, a, b, b, c, wherea, b, andc are all distinct.)
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Mission IIT Screening Test
Raju and Rani are playing betting game. Raju rolls a dice and if 5 comes on face then they stop the game, else Raju needs to pay 1 rupee ro Rani and continue rolling. Expected no of rupees Rani gets in this game?
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6 days
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probability ques
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probability
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Mission IIT Screening Test
In a group of $11$ people what is the probability that at least two people have birthday on same day ?
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Probability
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generalaptitude
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11
GATE201027
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$? $\left(\dfrac{1}{625}\right)$ $\left(\dfrac{4}{625}\right)$ $\left(\dfrac{12}{625}\right)$ $\left(\dfrac{16}{625}\right)$
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Jun 11
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gate2010
probability
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12
GATE 2015 EE How to find which coin is fair?
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Jun 10
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probability
gate2015ee
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TIFR2011A9
You have to play three games with opponents $A$ and $B$ in a specified sequence. You win the series if you win two consecutive games. $A$ is a stronger player than $B$. Which sequence maximizes your chance of winning the series? $AAB$ $ABA$ $BAB$ $BAA$ All are the same.
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Jun 3
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muthu kumar
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tifr2011
probability
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14
Bayes Probability Question
URN I contains 3 White,2 Black 2 Green Balls. URN II contains 2 White,3 Black 4 Green Balls. URN III contains 5 White,2 Black 2 Green Balls. An urn is chosen at random and two balls are drawn,they happen to be black and green. What is the probability that the come from urns 1) URN I 2) URN II 3) URN III ????
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Jun 1
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Made easy test
Consider Ramesh purchase a product of Patanjali. The manual on it states that the lifetime $T$ of product is defined as the amount of time (in years) the product works properly until it breaks down, satisfy following equation : $$P(T \geq t) = e^{t/4}, \text{for all } t \geq 0$$ The probability that it breaks down in $3^{rd}$ year is ______. (Upto $2$ decimal places)
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May 31
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saumya mishra
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engineeringmathematics
probability
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16
CMI2014A02
The $12$ houses on one side of a street are numbered with even numbers starting at $2$ and going up to $24$. A free newspaper is delivered on Monday to $3$ different houses chosen at random from these $12$. Find the probability that at least $2$ of these newspapers are delivered to houses ... strictly greater than $14$. $\frac{7}{11}$ $\frac{5}{12}$ $\frac{4}{11}$ $\frac{5}{22}$
answered
May 26
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mehul vaidya
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cmi2014
probability
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17
#cdssampleTest
One in two hundred people in a population have a particular disease. A test is developed for the disease. The test gives a false positive $3\%$ of the time (i.e. reports that a person has the disease even when he/she does not), and a false ... disease even when he/she does). Rahul takes the test and the report comes positive. What is the probability that Rahul has the disease?
answered
May 25
in
Probability
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Sumeet Singh
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381
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110
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engineeringmathematics
probability
0
votes
2
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18
Probability
The chances that doctor A will diagnose a disease X correctly is 60%. The chances that a patient will die by his treatment after correct diagnosis is 40% and the chances of death by wrong diagnosis is 70%. A patient of doctor A, who had disease X, died. The chances that his disease was diagnosed correctly is ________%.
answered
May 24
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Probability
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Subarna Das
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91
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probability
engineeringmathematics
+10
votes
11
answers
19
TIFR2012A1
Amar and Akbar both tell the truth with probability $\dfrac{3 } {4}$ and lie with probability $\dfrac{1}{4}$. Amar watches a test match and talks to Akbar about the outcome. Akbar, in turn, tells Anthony, "Amar told me that India won". What probability should Anthony ... left(\dfrac{6 }{16}\right)$ $\left(\dfrac{7}{16}\right)$ $\left(\dfrac{10}{16}\right)$ None of the above
answered
May 22
in
Probability
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mehul vaidya
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673
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tifr2012
probability
conditionalprobability
0
votes
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20
Probability Density Function
Given a probability density function $\frac{1}{x}$. Value exists in the interval $\left ( 2,3 \right )$ Can this pdf has existence outside this range?
asked
May 18
in
Probability
by
srestha
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45
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probability
engineeringmathematics
+1
vote
1
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21
CMI 2018 Objective
Suppose Kn be the number of strings having n X's and n Y's such that in all the prefixes of a string the number of X's is greater than the number of Y's. Now suppose you are standing at an edge of a swimming pool. You have a bag of n red and n blue balls.Now you are ... the probability that you will not get wet. A) Kn / (2nCn) B) n Kn / (2nCn) C) Kn / (2n)! d) n kn / 22n
answered
May 17
in
Probability
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Kushagra Chatterjee
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86
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probability
usercmi2018
usermod
0
votes
2
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22
CMI 2018 (Probability)
Suppose you have two coins $A$ and $B$ the probability of head in $A$ is $\dfrac{1}{4}$ and the probability of head in $B$ is $\dfrac{3}{4}$. Now, suppose you have chosen a coin and tossed it two times. The output was head and head. What is the probability that you chose the coin $B$.
answered
May 17
in
Probability
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ankitgupta.1729
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usercmi2018
usermod
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vote
1
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23
Probability
I toss a coin repeatedly. The coin is unfair and P(H) = p. The game ends the first time that two consecutive heads (HH) or two consecutive tails (TT) are observed. I win if HH is observed and lose if TT is observed. For example if the outcome is HTHTT, I lose. On the other hand, if the outcome is THTHTHH, I win. Find the probability that I win. Ans: $\frac{p^{2} (2p)}{(1p+p^{2} )}$
answered
May 15
in
Probability
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amit1
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635
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62
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probability
engineeringmathematics
discretemathematics
+11
votes
6
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24
GATE20033
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are $\left(\dfrac{1}{4}\right),\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{2}\right),\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{2}\right),{1}$ ${1},\left(\dfrac{1}{2}\right)$
answered
May 15
in
Probability
by
Jeevesh
(
155
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1.5k
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gate2003
probability
easy
conditionalprobability
+15
votes
3
answers
25
GATE201133
Consider a finite sequence of random values $X=[x_1,x_2,\dots x_n]$. Let $\mu_x$ be the mean and $\sigma_x$ be the standard deviation of $X$. Let another finite sequence $Y$ of equal length be derived from this as $y_i=a*x_i+b$, where $a$ and $b$ are positive constants. Let ... in $X$ is the same as the index position of median of $Y$ in $Y$ $\mu_y=a \mu_x + b$ $\sigma_y=a \sigma_x + b$
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May 11
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srestha
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gate2011
probability
randomvariable
normal
0
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2
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26
Bayes theorem
This is extended form of Bayes theorem Can somebody explain (or can prove), how from 1st line 2 line came?
answered
May 11
in
Probability
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Ayush Upadhyaya
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probability
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27
Modification of GATE question
A coin tossed 3 times 1) if output at last two toss is $HT$ then stop tossing 2) if output of last two toss is $TT$ then toss again and go to step 1 or step 3 3) if output of last two toss is $TH$ or $HH$ then toss again and goto step 2 What will be probability, that at last the coin will stop tossing?
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May 9
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probability
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votes
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28
IIT M Written : Probability
An experiment is performed $n$ times, in each of which an event $X$ may occur with a probability $p$. Determine$ E[ \overline{X}]$ and $Var( \overline{X})$, where $\overline{X} $is the complement of the event $X$
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May 7
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Probability
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Sourajit25
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writtentest
iitmadras
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expectedvalue
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votes
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29
IIT M Written Test
Any Hints on how to solve this?
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Probability
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Sourajit25
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writtentest
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linearregression
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30
Doubt
Suppose we are playing a game.You have to choose 1 out 3 doors.Behind 1 lucky door ,we have 1 million dollars.You picked 1 st door.But i opened the 3rd door and found nothing.Now,if i give you another chance ,will you change your choice? (Use probabiliy estimates to answer)
answered
May 6
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Probability
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probability
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votes
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31
Universality of Uniform
According to Universality of Uniform , We can get from the uniform distribution to the other distributions and also from other distributions back to the uniform distribution. Please explain how we would simulate from one distribution to other distribution ?
[closed]
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May 6
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ankitgupta.1729
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randomvariable
uniformdistribution
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votes
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32
Total probability and Baye's theorem
When we should use Total probability and Baye's Theorem? Explain with examples.
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May 5
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Probability
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Devbrat Sharma
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105
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probability
engineeringmathematics
conditionalprobability
+2
votes
1
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33
IISc CDS(MTech R)
There are 12 pair of shoes, what is the probability that atleast one complete pair of shoes are present if 4 shoes are selected at random?
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May 4
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iisc
cds
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34
Intermediate Conting and Probability(David Patrick)
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Intermediate Conting and Probability
Solve
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A First Course in Probability 8th Edition: Axioms of Probability Example 5k
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permutationsandcombinations
sheldonross
probability
engineeringmathematics
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37
IIT Kanpur Test Sample Paper
(Overfed pets) The Jones family have n pet cats. The caretaker who is charged to feed these cats is very careless. Everytime he goes into the pet zone, he takes food along and feeds a random cat  he does not care whether the cat seems to be hungry ... expectation, how many more trips would he have to make before he feeds one of the unfed (n− k) cats for the first time?
answered
Apr 29
in
Probability
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iitkanpur
writtentest
mtech
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38
IIT Kanpur Test Sample Paper
(Batman and Robin) The city of Gotham keeps propping up newer challenges for our dynamic duo. The criminals in the city are so organized that they have come up with a schedule to commit the crimes. a. The Mad Hatter commits maddeningly despicable ... . What is the probability of that? 4) In the above scenario, what is the probability that two criminals get defeated?
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Apr 29
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iitkanpur
writtentest
mtech
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4
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39
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
Apr 27
in
Probability
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mehul vaidya
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tifr2013
probability
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40
Probability
Prove for a positive integer valued random variable, $X$ , and for positive integers $a < b$ \begin{align*} &P(X \geq b) \leq \left [ \left ( \frac{E(X)}{b} \right )  P(a \leq X < b)\cdot \left ( \frac{a}{b} \right ) \right ] \\ \end{align*}
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Apr 27
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Probability
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