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Recent questions and answers in Probability
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Sheldon Ross, Chapter #4, Question #13
An airline operates a flight having 50 seats. As they expect some passenger to not show up, they overbook the flight by selling 51 tickets. The probability that an individual passenger will not show up is 0.01, independent of all other ... the airline has to pay a compensation of Rs.1lakh to that passenger. What is the expected revenue of the airline?
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ISI2019MMA22
A coin with probability $p (0 < p < 1)$ of getting head, is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $2/5$, then the value of $p$ is $2/7$ $1/3$ $5/7$ $2/3$
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May 16
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ISI2018MMA18
Let $A_1 = (0, 0), A_2 = (1, 0), A_3 = (1, 1)\ $and$\ A_4 = (0, 1)$ be the four vertices of a square. A particle starts from the point $A_1$ at time $0$ and moves either to $A_2$ or to $A_4$ with equal probability. Similarly, in each of the subsequent ... $T$ be the minimum number of steps required to cover all four vertices. The probability $P(T = 4)$ is $0$ $1/16$ $1/8$ $1/4$
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May 16
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isi2018
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4
Ace Test Series: Probability  Uniform Distribution
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May 15
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GATE 2015 SET2 Q 29
Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is _______.
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May 14
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ISI2018MMA20
Consider the set of all functions from $\{1, 2, . . . ,m\}$ to $\{1, 2, . . . , n\}$,where $n > m$. If a function is chosen from this set at random, the probability that it will be strictly increasing is $\binom{n}{m}/n^m\\$ $\binom{n}{m}/m^n\\$ $\binom{m+n1}{m1}/n^m\\$ $\binom{m+n1}{m}/m^n$
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May 12
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ISI2018MMA17
There are eight coins, seven of which have the same weight and the other one weighs more. In order to find the coin having more weight, a person randomly chooses two coins and puts one coin on each side of a common balance. If these two coins are found to have the same ... as before. The probability that the coin will be identified at the second draw is $1/2$ $1/3$ $1/4$ $1/6$
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May 12
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8
ISI2018MMA16
Consider a large village, where only two newspapers $P_1$ and $P_2$ are available to the families. It is known that the proportion of families not taking $P_1$ is $0.48$, not taking $P_2$ is $0.58$, taking only $P_2$ is $0.30$. The probability that a randomly chosen family from the village takes only $P_1$ is $0.24$ $0.28$ $0.40$ can not be determined
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May 11
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9
ISI2019MMA10
The chance of a student getting admitted to colleges $A$ and $B$ are $60\%$ and $40\%$, respectively. Assume that the colleges admit students independently. If the student is told that he has been admitted to at least one of these colleges, what is the probability that he has got admitted to college $A$? $3/5$ $5/7$ $10/13$ $15/19$
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May 7
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isi2019
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Gate 2018: Probability
In a box, there are $2$ red, $3$ black and $4$ blue coloured balls. The probability of drawing $2$ blue balls in sequence without replacing, and then drawing $1$ black ball from this box is _________ %.
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May 1
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GATE2016129
Consider the following experiment. Step 1. Flip a fair coin twice. Step 2. If the outcomes are (TAILS, HEADS) then output $Y$ and stop. Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output $N$ and stop. Step 4. If the outcomes are (TAILS, TAILS), then go to Step 1. The probability that the output of the experiment is $Y$ is (up to two decimal places)
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Apr 23
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gate20161
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12
GATE2008IT23
What is the probability that in a randomly chosen group of $r$ people at least three people have the same birthday? $1\dfrac{365364 \dots (365r+1)}{365^{r}}$ ... $\dfrac{365 \cdot 364 \dots (365r+1)}{365^{r}}$
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Apr 22
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Probability of error detection
A block of bits with n rows and m columns uses horizontal and vertical parity bits for error detection. If exactly 4 bits are in error during transmission, derive an expression for the probability that the error will be detected.
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Apr 20
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CMI Data Science 2018 (Probability)
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15
ISI paper
A block of bits with n rows and m columns uses horizontal and vertical parity bits for error detection. If exactly 4 bits are in error during transmission, derive an expression for the probability that the error will be detected.
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Apr 18
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Probability
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+9
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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 ... probability that it came from the box $P$ is: $\dfrac{4}{19}$ $\dfrac{5}{19}$ $\dfrac{2}{9}$ $\dfrac{19}{30}$
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Apr 15
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Rishi yadav
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gate2005
probability
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17
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?
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Apr 14
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Probability
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0
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18
PGCET2010CS
The expected value of a probability function, when probability is measured on a scale of 0 to 1, coincides with it's (a) Mean (b) Variance (c) Standard deviation (d) None of them
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Apr 9
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Probability
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Prajna
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1
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19
sheldon ross, chapter 2, question 17
If 8 rooks are randomly placed on a chessboard, compute the probability that none of the rooks can caputre any of the others. That is compute the probability that no row or file contains more than one rook.
answered
Apr 8
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Asim Siddiqui 4
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138
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discretemathematics
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5
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20
ISI2017MMA21
There are four machines and it is known that exactly two of them are faulty. They are tested one by one in a random order till both the faulty machines are identified. The probability that only two tests are required is $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{6}\right)$
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Apr 2
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amanpandey007
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495
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isi2017
engineeringmathematics
probability
0
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21
SHELDON AND ROSS
Twelve percent of all US households are in California. A total of 3.3 percent of all US households earn over 250000 per year, while a total of 6.3 percent California households earn over 250000 per year. If a randomly chosen US household earns over 250,000 per year, ... 10^(3)/(0.033)=0.2291 But the answer given in the instructors manual is .2066 What is wrong with my logic??
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Mar 22
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Probability
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Doraemon
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203
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32
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probability
sheldonross
0
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4
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22
ISRO2012ECE Probability
Person X can solve 80% of the ISRO question paper and Person Y can solve 60%. The probability that at least one of them will solve a problem from the question paper, selected at random is : a. 0.48 b. 0.70 c. 0.88 d. 0.92
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Mar 10
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isro2012ece
isroece
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0
votes
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23
Zeal Test Series 2019: Probability  Probability
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Mar 9
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24
Probability  Independent Events
What is the probability that, in six throws of a die, there will be exactly one each of “1”, “2”, “3”, “4”, “5” and “6”? $0.00187220$ $0.01432110$ $0.01176210$ $0.01543210$
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Mar 8
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zeeshanmohnavi
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857
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engineeringmathematics
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vote
2
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25
ISRO 2014 probability [EE]
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is (A) 140 (B) 196 (C) 280 (D) 346
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Mar 7
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Probability
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abhishekmehta4u
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350
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isroee
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probability
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1
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26
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?
answered
Mar 1
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Probability
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conditionalprobability
+16
votes
3
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27
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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Feb 21
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gate1998
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4
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28
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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Feb 21
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gate20172
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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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Feb 20
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gate2011
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30
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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Feb 20
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31
Discrete random variable
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Feb 20
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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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Feb 19
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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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Feb 19
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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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Feb 19
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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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Feb 19
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JEST 2019
Three dice are rolled independently. Probability of obtaining the difference from largest and smallest number as exactly 4 :
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Feb 18
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Satbir
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37
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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Feb 18
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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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39
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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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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