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Recent questions and answers in Probability
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GATE19983a
Two friends agree to meet at a park with the following conditions. Each will reach the park between 4:00 pm and 5:00 pm and will see if the other has already arrived. If not, they will wait for 10 minutes or the end of the hour whichever is earlier and leave. What is the probability that the two will not meet?
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gate1998
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2
GATE2017248
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
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gate20172
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3
GATE201118
If the difference between the expectation of the square of a random variable $\left(E\left[X^2\right]\right)$ and the square of the expectation of the random variable $\left(E\left[X\right]\right)^2$ is denoted by $R$, then $R=0$ $R<0$ $R\geq 0$ $R > 0$
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gate2011
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Grewal
Suppose avg waiting time of a process to get chance in a queue is 5 min. What will the probability that process get chance at first minute is ________________
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3 days
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Probability
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Discrete random variable
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Central limit theorem
(Central Limit Theorem) Let X1, X2, . . . , X81 be i.i.d., each with expected value µ = E(Xi) = 5, and variance σ2 = Var(Xi) = 4. Approximate P(X1 + X2 +· · · X81 > 369), using the central limit theorem.
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Probability mass function
Suppose that the cdf of X is given by: F(a) ={ 0 for a < 0 1/5 for 0 ≤ a < 2 2/5 for 2 ≤ a < 4 1 for a ≥ 4. } Determine the pmf of X.
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Probability density function
Let R be the rate at which customers are served in a queue. Suppose that R is exponential with pdf f(r) = 2e^(−2r) on [0, ∞). Find the pdf of the waiting time per customer T = 1/R.
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Expectation
Suppose 100 people all toss a hat into a box and then proceed to randomly pick out a hat. What is the expected number of people to get their own hat back. Hint: express the number of people who get their own hat as a sum of random variables whose expected value is easy to compute.
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10
JEST 2019
Three dice are rolled independently. Probability of obtaining the difference from largest and smallest number as exactly 4 :
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Probability
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Satbir
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jest
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11
Conditional Probability
A multiple choice exam has 4 choices for each question. A student has studied enough so that the probability they will know the answer to a question is 0.5, the probability that they will be able to eliminate one choice is 0.25, otherwise ... the test to measure what the student knows. If the student answers a question correctly what's the probability they knew the answer?
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Conditional probability
Oscar has lost his dog in either forest A (with a priori probability 0.4) or in forest B (with a priori probability 0.6). On any given day, if the dog is in A and Oscar spends a day searching for it in A, the conditional probability that he will ﬁnd the dog that day is 0.25. ... +(1/2)*0.15; but the answer given is=(0.5*0.4*0.25)+(0.5*0.6*0.15); what is wrong with my logic?
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Feb 16
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DIYA BASU
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3
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13
TIFR2011MathsB10
Suppose a box contains three cards, one with both sides white, one with both sides black, and one with one side white and the other side black. If you pick a card at random, and the side facing you is white, then the probability that the other side is white is $1/2$.
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Feb 16
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Probability
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14
JEST Sample Question 1c
If a fair die (with 6 faces) is cast twice, what is the probability that the two numbers obtained differ by 2? (A) 1/12 (B) 1/6 (C) 2/9 (D) 1/2
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Feb 15
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Probability
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JEST Sample Question6
Two gamblers have an argument. The first one claims that if a fair coin is tossed repeatedly, getting two consecutive heads is very unlikely. The second, naturally, is denying this. They decide to settle this by an actual trial; if, within n coin tosses, ... demonstrated. What happens for larger values of n? Is it true that P (n) only increases with n? Justify your answer.
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Feb 15
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Sheldon ross example 5f
A poker hand consists of 5 cards.If the cards have distinct consecutive values and are not all of the same suit,we say that hand is straight.For instance a hand consisting of the five of spades,six of spades,seven of spades,eight of spades and nine of hearts is a straight.What is the probability that one is dealt is a straight?
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Feb 14
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Probability
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17
Probability
Bob has a peculiar pair of foursided dice. When he rolls the dice, the probability of any particular outcome is proportional to the sum of the results of each die. All outcomes that result in a particular sum are equally likely. (a) What is the probability of the ... Here what do we mean by the line  any particular outcome is proportional to the sum of the results of each die.
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Feb 14
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Probability
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ck
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probability
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18
A family has two children. Given that one of the children is a boy, what is the probability that both children are boys?
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Feb 14
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probability
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19
Probability
Let 3 cards are drawn from a pack of 52 cards one by one without replacement then find the prob that 3 cards are drawn out of which 2 are ace Ace and one is King?
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Feb 13
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Probability
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rtalwar
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64
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0
votes
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20
Expectation
How is E[X1/X>1]=E[X]. Please explain.
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Feb 12
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Probability
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DIYA BASU
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241
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26
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0
votes
3
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21
GATE 2019 23
Q.23 Two numbers are chosen independently and uniformly at random from the set (1, 2,..., 13]. The probability (rounded off to 3 decimal places) that their 4bit (unsigned) binary representations have the same most significant bit is
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Feb 12
in
Probability
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mkagenius
(
329
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448
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usergate2019
usermod
probability
numericalanswers
normal
+2
votes
3
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22
Uniform probability distribution
X is uniformly distributed random variable that takes values between 0 and 1.The value of E(X^3) will be
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Feb 12
in
Probability
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Shashi Shekhar 1
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557
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685
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randomvariable
expectation
+1
vote
3
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23
GATE201947
Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only rela roots is (rounded off to $1$ decimal place) _______
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Feb 12
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24
Sheldon and Ross
Two balls each equally likely to be colored either red or blue, are put in an urn. At each stage one of the balls is randomly chosen, its color is noted, and it is then returned to the urn.if the first two balls chosen are colored red, what is the probability that a>both balls in the urn are colored red b>the next ball chosen will be red how to solve this?
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Feb 7
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DIYA BASU
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241
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50
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25
query
Can someone provide me with the names of good resources for continuous random variable?
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Feb 6
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27
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26
SHELDON AND ROSS
FOR Q30 WHAT IS THE ANSWER??
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Feb 4
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83
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27
Self doubt
Suppose 3 batteries are choosen at random from a group of 3 new and 4 used but still working and 5 ddefective batteries what is the probability of choosing 3 defective batteries? why is(5C3)/(12C3 ) the correct answer and (5*4*3)/(12C3) not the correct answer??
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Feb 3
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Probability
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69
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votes
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28
Uniform Distribution
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Feb 2
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Na462
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59
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randomvariable
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acetestseries
+9
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5
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29
GATE20022.16
Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is $\frac{1}{16}$ $\frac{1}{8}$ $\frac{7}{8}$ $\frac{15}{16}$
answered
Jan 28
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Probability
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Sambhrant Maurya
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2.2k
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gate2002
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30
Gate 2014 ec
A fair coin is tossed repeatedly till both head and appear atleast once. The average number of tosses required is?
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Jan 26
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Probability
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401
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31
GATEEY2018 Q53
The probability that a bush has a cricket is 0.1. The probability of a spider being present on a bush is 0.2. When both a spider and a cricket are present on a bush, the probability of encountering each other is 0.2. The probability of a spider consuming a ... a cricket is preyed on by a spider is ____ (answer up to 3 decimal places). Is it multiplication of everything i.e. 0.002.
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Jan 26
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Probability
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32
Made easy test series probability
A dice is tossed thrice. A success is getting ‘1 or 6' on a toss. Find the variance of number of successes _. Answer 0.66
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Jan 24
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33
Applied Course Mock Test 4
Q32 [Mock 4]. Naveen's coin box contains 8 fair standard coins (heads and tails) and 1 coin which has heads on both sides. He selects a coin randomly and flips it 4 times, getting all heads. If he flips this coin again, what is the probability it ... )+(1/9)*(1) Probability of choosing fair coin and P(heads)+ P(unfair)*P(heads). Please help me understand this question.
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Jan 22
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34
probability
Probability density function of a random variable X is distributed uniformly between 0 and 10 The probability that X lies between 2.5 to 7.5 and the mean square value of X are respectively. please give step by step answer in a detailed manner.
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Jan 21
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35
Gateforum mock 2
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Jan 20
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Probability
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gateforumtestseries
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36
probability
A treasure has 6 similar gold coins and 9 silver coins. If 4 coins are to be randomly selected without replacement, the probability that the first 2 selected are gold and the last 2 silver
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Jan 19
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Probability
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37
Probability
Suppose that a bag contains 8 blue cubes and 4 green cubes. We draw 2 cubes from the bag without replacement. It is given that blue balls are of weight 1Kg and green balls are of weight 0.5 Kg. Suppose that the probability that a given cube in the bag ... is its weight divided by the sum of the weights of all cubes currently in the bag. What is the probability that both cubes are blue.
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Jan 19
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Probability
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probability
engineeringmathematics
0
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38
GATEBOOK2019 Mock Test137
In an examination there are $80$ questions each having four choices. Exactly one of these four choices is correct and the other three are wrong. A student is awarded $1$ mark for each correct answer, and $0.25$ for each wrong answer. If a student ticks ... each question randomly, then the expected value of his/her total marks in the examination is. $15$ $0$ $5$ $20$
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Jan 19
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made easy test series question on Probability
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40
Dice problem (Made easy)
Can any one explain me the part in green box Thanks :)
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Jan 16
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