10 Question MCQ (including Assertion)

Two unbiased coins are tossed. If one coin shows head, the probability that the other also shows head is \(\_\_\_\_\)

Each child is equally likely to be a boy or girl. For a randomly chosen three-child family, the probability that the eldest child is a girl given that the family has at least one girl is

If \(P(A\cap B)=7/10\) and \(P(B)=17/20\), then \(P(A\mid B)\) equals

Let \(P(A)=7/13\), \(P(B)=9/13\), and \(P(A\cap B)=4/13\). Then \(P(A^{\prime}\mid B)\) is equal to

If \(A\) and \(B\) are independent events such that \(0<P(A)<1\) and \(0<P(B)<1\), then which of the following is not correct?

For the probability distribution below, \(E(X)\) is equal to

Let \(P(A)=3/8\), \(P(B)=5/8\), and \(P(A\cup B)=3/4\). Then \(P(A\mid B)P(A^{\prime}\mid B)\) equals

If events \(A\) and \(B\) are independent, then \(P(A\cap B)\) is equal to

Which one is not a requirement of a binomial distribution?