If $A$ and $B$ are independent events such that $0 < P(A) < 1$ and $0 < P(B) < 1$, then identify the correct statements.

(A) $A$ and $B'$ are independent

(B) $A'$ and $B$ are independent

(C) $A$ and $B$ are mutually exclusive

(D) $A'$ and $B'$ are independent

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4 cards are drawn from a standard deck of 52 cards. The probability of drawing exactly 2 cards of the same suit is:

If $X$ is a normal variate with mean 12 and standard deviation 4, then $P[X \ge 20]$ is:

[Given that: $P[0 \le Z \le 2] = 0.4772]$

Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probability, that both coins are unbiased is:

If E and F are two independent events such that $P(E)=\dfrac{1}{3}, P(F)=\dfrac{3}{5}$, then which of the following is/are correct ?

A. $P(E \cap F) = \dfrac{1}{5}$

B. $P\left(\dfrac{\overline{E}}{F}\right) = \dfrac{2}{3}$

C. $P\left(\dfrac{E}{\overline{F}}\right) = \dfrac{2}{3}$

D. $P\left(\dfrac{E}{F}\right) = \dfrac{2}{3}$

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A random variable X has the following probability distribution:

The value of E(X) is:

A pair of coins thrown then

Match the LIST-I with LIST-II

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