If $P(A) = 0.4$, $P(B) = X$ and $P(\bar{A} \cap \bar{B}) = 0.4$, where A and B are independent event, then the value of X is:

The random variable X can take values 0, 1, 2. If $P(X=0)=P(X=1)=\alpha$, and $E(X^2)=E(X)$, then which of the following are correct?

(A) $E(X) = 2-3\alpha$

(B) $E(X^2) = 4+7\alpha$

(C) $\alpha = \frac{1}{2}$

(D) $\alpha = \frac{1}{5}$

Choose the correct answer from the options given below:

A dice is thrown twice, the probability of occurence of 5 at least once is

For any two events A and B, which of the following are correct?

(A) $P(A\cup B) = P(A)+P(B)-P(A\cap B)$

(B) $P(A) = P(A\cup B)+P(A\cap B)$

(C) $P(A/B) = P(A)/P(B)$

(D) $P(A) = P(A\cap B)+P(A\cap \bar{B})$

Choose the correct answer from the options given below:

A box contains 3 red and 2 black balls and another box contains 2 red and 4 black balls. One box chosen at random. From the selected box one ball is drawn. The probability of getting a red ball is

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Then variance of the number of kings is

One person speaks truth in 60% of the cases and another person in 80% of the cases. They are likely to agree in stating the same fact in