List of top Statistics Questions on Probability theory

A simple random sample of size 'n' will be drawn from a class of 125 students, and mean mathematics score of the sample will be compute
D. If the standard error of the sample mean for "with replacement sampling" is twice as much as the standard error of the sample mean for "without replacement sampling", then the value of n is

Value of $\lim_{n \rightarrow \infty} e^{-n}\left(1+n+\frac{n^{2}}{2 !}+\dots+\frac{n^{n}}{n !}\right)$ is

A joint density function of random variable $X$ and $Y$ is given by $f(x,y)=\begin{cases}kx & \text{for } 0<x<1, 0<y<1 \\ 0 & \text{otherwise}\end{cases}$ then $Cov(X,Y)$ is

Let E, F and G be events such that $P(E|G) = 0.05$ and $P(F|G) = 0.05$ which of the following statement must be true?

A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club President would like to know how many members regularly use each facility. A survey of the membership indicates that 61% regularly use the golf course, 45% regularly use the tennis courts, and 3% use neither of these facilities regularly. What percentage of the 600 uses at least one of the golf or tennis facilities?

What is the probability of getting seventh head in the tenth toss of an unbiased coin?

In a university, 50% of the students choose a movie, 30% choose dinner and a play, and 20% choose shopping as a leisure activity. If a sample of 5 students is randomly selected, what is the probability that 3 are planning to go to a movie, 1 to a play, and 1 to a shopping mall?

A cold drinks bottling plant produces 1% defective bottles. The probability that there will be no defective in a lot of 100 bottles is nearest to:

The statements below relate to Bayes theorem in probability:

(i) Bayes theorem gives a formula to compute conditional probability.
(ii) The posterior probability computed by Bayes theorem supersedes the prior probability.
(iii) Bayes theorem can be used to compute probabilities of past events on the basis of the occurrences of subsequent events.

Identify the correct answer:

If \(P(A) = 0.25\), \(P(B|A) = 0.5\), \(P(B|\bar{A}) = 0.75\) then \(P(A|B)\) is ______.

A card is drawn at random from a standard deck of 52 cards. Then, the probability of getting either an ace or a club is:

A six-faced die is rolled twice. Then the probability that an even number turns up at the first throw, given that the sum of the throws is 8, is