# Recent questions tagged probability

0 votes
1 answer 24 views
In how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together?
0 votes
0 answers 62 views
There are 100 rooms in a hotel. The hotel manager is lazy. When a customer requests a room, the manager picks a room from 1 to 100 uniformly at random without even bothering to check whether it is already occupied. If the room is already occupied, the customer is asked ... that 100 customers try to check in, one by one, to the hotel. Show that the expected number of occupants is at least 50.
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0 answers 10 views
Consider a random chord of a circle. What is the probability that the length of the chord will be greater than the side of the equilateral triangle inscribed in that circle?
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1 answer 13 views
When switching the CPU between two processes.. which of the following applies A. The PCB is both, saved and reloaded, only for the interrupted process that is existing the CPU B. The PCB is saved for the process that is scheduled for the CPU C. The PCB is reloaded for the process that is scheduled for the CPU D. No PCB is saved or reloaded E. None of the above
0 votes
0 answers 12 views
consider an urn with ‘a’ red and ‘b’ blue ball . Balls are drawn out one by one without replacement uniformly at random until the first red ball is drawn .what is expected no of ball drawn?
0 votes
0 answers 14 views
Lavanya and Ketak each flip a fair coin (i.e., both heads and tails have equal probability of appearing) $n$ times. What is the probability that Lavanya sees more heads than Ketak? In the following, the binomial conefficient $n\choose k$ counts the number of $k$-element subsets of an $n$ ... $\sum_{i=0}^{n}\frac{{n\choose i}}{2^{2n}}$
0 votes
0 answers 11 views
A matching in a graph is a set of edges such that no two edges in the set share a common vertex. Let $G$ be a graph on $n$ vertices in which there is a subset $M$ of $m$ edges which is a matching. Consider a random process where each vertex in the graph is independently selected with probability $0 < p < 1$ and let $B$ ... $1 - (1 - p^2)^m$ (C) $p^{2m}$ (D) $(1 - p^2)^m$ (E) $1 - (1 - p(1 - p))^m$
0 votes
0 answers 11 views
What is the probability that at least two out of four people have their birthdays in the same month, assuming their birthdays are uniformly distributed over the twelve months? (A) $\frac{25}{48}$ (B) $\frac{5}{8}$ (C) $\frac{5}{12}$ (D) $\frac{41}{96}$ (E) $\frac{55}{96}$
0 votes
1 answer 33 views
A random variable X which takes two values 0 and 1 with probability q and p respectively. Let P(X=1)=p and P(X=0)=q, q=1-p Show that E(X)=p and Var(X)=pq Find the Mgf of X
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0 answers 16 views
1 vote
0 answers 35 views
Consider a binomial experiment of flipping a biased coin five times with probability of head ,p=0.75 and probability of tail q=0.25 in each flip. What is the probability that last two flips will be heads if the first three flips are known to be tails ?
4 votes
1 answer 656 views
For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________
3 votes
3 answers 842 views
In an examination, a student can choose the order in which two questions ($\textsf{QuesA}$ and $\textsf{QuesB}$) must be attempted. If the first question is answered wrong, the student gets zero marks. If the first question is answered correctly and the second question is not ... and then $\textsf{QuesA}$. Expected marks $22$. First $\textsf{QuesA}$ and then $\textsf{QuesB}$. Expected marks $16$.
4 votes
4 answers 1.3K views
A bag has $r$ red balls and $b$ black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will ...
2 votes
1 answer 1.2K views
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is __________ $0.3024$ $0.4235$ $0.6976$ $0.8125$
2 votes
2 answers 794 views
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.
1 vote
1 answer 582 views
Consider the two statements. $S_1:\quad$ There exist random variables $X$ and $Y$ such that $\left(\mathbb E[(X-\mathbb E(X))(Y-\mathbb E(Y))]\right)^2>\textsf{Var}[X]\textsf{Var}[Y]$ $S_2:\quad$ For all random variables $X$ ... Both $S_1$ and $S_2$ are true $S_1$ is true, but $S_2$ is false $S_1$ is false, but $S_2$ is true Both $S_1$ and $S_2$ are false
3 votes
2 answers 670 views
A sender $(\textsf{S})$ transmits a signal, which can be one of the two kinds: $H$ and $L$ with probabilities $0.1$ and $0.9$ respectively, to a receiver $(\textsf{R})$. In the graph below, the weight of edge $(u,v)$ is the probability of receiving $v$ ... $0.7$. If the received signal is $H,$ the probability that the transmitted signal was $H$ (rounded to $2$ decimal places) is __________.
0 votes
1 answer 24 views
A bag contains 5 black, 2 red and 3 white marbles. Three marbles are drawn simultaneously. The probability that the drawn marbles are of the different color is ?
1 vote
1 answer 38 views
A box contains 10 apples out of which 4 are rotten. Two apples are taken out together if one of them is good what is the probablity that the other one is also good. Note: Please don’t use ‘C’ combination terms in your answer rather try to make it as clear as possible.
0 votes
0 answers 31 views
In this previous year question https://gateoverflow.in/179371/, can someone PLEASE explain why is it wrong to say that if i have probability of success = $\frac{1}{26^{10}}$ ... selected answer? Please give a proper reason like, the reason why we can't say the answer is B is because checking is a dependent event.
0 votes
1 answer 44 views
Let there are $n$ devices in the setup. Let each device sends data with a probability $p$ ... (Simply because in the $\dagger$ they assume $c=e$ which is not correct. Which is the correct one and which one to follow?
0 votes
0 answers 38 views
The probability of number of defectives in a lot is 35%. There are 4 items taken out with replacement. Find the probability that none of the items are defective?
0 votes
1 answer 29 views
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6 . What is the probability that he will knock down fewer than 2 hurdles?
1 vote
1 answer 50 views
Find the probability that at most 2 heads and at most 2 tails occur when 4 coins are tossed simultaneously?
0 votes
0 answers 23 views
A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.
1 vote
1 answer 42 views
Balls are drawn one after the other uniformly at random without replacement from a set of eight balls numbered 1,2,...,8 until all balls drawn what is expected number of balls whose value matched their ordinality (i.e their position in the order in which balls were drawn ... the probability that the i-th ball is drawn at the i-th draw ? now can you use linearity of expectation to solve the problem
0 votes
0 answers 21 views
How to solve this calculation step by step ? Ans is 99.56%.
0 votes
0 answers 19 views
What is Exponential Distribution in Probability?? Please discuss it with example!!! Thank you!!!
0 votes
0 answers 16 views
What is Uniform Distribution in Probability?? Please discuss it with example!!! Thank you!!!
1 vote
1 answer 56 views
1 vote
4 answers 256 views
In a family with 4 children, what is the probability of a 2:2 boy-girl split?
0 votes
1 answer 47 views
Six people, including A,B, and C, form a queue in a random order (all 6! orderings are equiprobable). Consider the event "B is between A and C in the queue". What is its probability? (The order of A and C can be arbitrary, but B should be between them).
0 votes
2 answers 387 views
Six people including A,B, and C, form a queue in a random order (all 6! orderings are equiprobable). Consider the event "A precedes B in the queue". (Again this event does not mention C or other people in the queue. It happens when A is closer to the start of the ... B, and does not require that B is the next after A, some people could be between A and B.) What is the probability of this event?
0 votes
2 answers 164 views
There is a test of Algorithms. Teacher provides a question bank consisting of N questions and guarantees all the questions in the test will be from this question bank. Due to lack of time and his laziness, Codu could only practice M questions. There are T questions in a ... of the T problems. Codu can't solve the question he didn't practice. What is the probability that Codu will pass the test?
0 votes
0 answers 18 views
A elevator manufacturing company believes that 'X' is the amount of that can elevator withstand without any damage with is mean 100 and standard deviation 10. This elevator is used to lift the company staff persons with mean 5 and standard deviation 0.5. How many staff person would have to be in the elevator for the probability of No damage exceeds to 0.85.
0 votes
1 answer 19 views
What are the Topics of Gravner that are related to GATE?
0 votes
1 answer 26 views
From a pack of 52 playing cards, three cards are drawn at random. The Probability of drawing a King, Queen and a jack can somebody please tell why is the following method wrong: (4/52)*(4/51)*(4/50) actual answer is 16/5525
0 votes
2 answers 27 views
Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students from a class of 30. How many different outcomes are possible if a student can receive any number of awards? //I do understand the approach that gives 30^5, but if someone can help me to point out the flaw in my approach.
0 votes
1 answer 101 views
A basketball team consists of 6 frontcourt and 4 backcourt players. If players are divided into roommates at random, what is the probability that there will be exactly two roommate pairs made up of a backcourt and a frontcourt player?