# Recent questions tagged probability

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?
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.
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?
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
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?
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 $n$ ... $\sum_{i=0}^{n}\frac{{n\choose i}}{2^{2n}}$
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) $1 - (1 - p(1 - p))^m$
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) $\frac{55}{96}$
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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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 ?
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 _________
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 $16$.
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 ...
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 __________ $0.3024$ $0.4235$ $0.6976$ $0.8125$
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 ____________.
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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
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 __________.
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 ?
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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.
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.
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?
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?
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?
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Find the probability that at most 2 heads and at most 2 tails occur when 4 coins are tossed simultaneously?
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.
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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
How to solve this calculation step by step ? Ans is 99.56%.
What is Exponential Distribution in Probability?? Please discuss it with example!!! Thank you!!!
What is Uniform Distribution in Probability?? Please discuss it with example!!! Thank you!!!
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In a family with 4 children, what is the probability of a 2:2 boy-girl split?
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).
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?
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?