Two numbers are selected at random (without replacement) from the first three positive integers. Let $X$ denotes the larger of the two integers, then the probability distribution of $X$ is

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. The probability distribution of number of aces is given by:

If A and B are event such that $P(A)=\dfrac{1}{2}$, $P(B)=p$ and $P(A \cup B)=\dfrac{3}{5}$ then which of following statements is/are TRUE?

(A) Events A and B are independent if $p=\dfrac{1}{5}$

(B) Events A and B are independent if $p \in (0,1) \sim \left\{\dfrac{1}{5}\right\}$

(C) Events A and B are independent then $P(A \cap B)=\dfrac{1}{10}$

(D) Event A and B are independent then $P(A \cap B)=\dfrac{9}{10}$

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If A, B and C are three independent events such that P(A)=P(B)=P(C)=x, then P(at least two of A, B, C occur) =

Let the random variable X represent the positive difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. Then probability $P(X \leq 3)$ is equal to

Let X denotes the number of heads in a simultaneous toss of three coins, then $P(0 < X < 3)$ is

A bag contains 4 balls. Let E be an event in which two balls are drawn at random and found to be white, then

Match List-I with List-II

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