A die is thrown and a coin is tossed. The probability that the outcome will be a number greater than 4 or a head or both is

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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Let A and B be two events such that $P(A \cap B) = 0$ then $P(A|(A \cup B))$ is equal to:

Let A and B be two independent events. Then which of following statements is not true?

Let A and B be two independent events such that $P(A)=k$, $P(B)=2k$ and probability of occurrence of exactly one of them is $\dfrac{5}{9}$. Then the value(s) of $k$ is/are:

Let X be a random variable. Let E (X) and Var (X) denote the mean and the variance of X respectively. Then match List-I with List-II

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If A and B are independent events such that $P(A|B) = \frac{1}{3}$ and $P(B) = \frac{1}{2}$, then the value of $P(A \cap B)$ is equal to