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) =

Two cards are drawn simultaneously at random from a well shuffled pack of 52 Cards. Let X be the random variable which denotes number of kings in the draw. Then the probability distribution of X is

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

A coin is tossed K times. If the probability of getting $3$ heads is equal to the probability of getting $7$ heads, then the probability of getting $8$ tails is :

Three students A, B and C can respectively solve 50%, 25% and 20% of the problems in a book. A particular problem is selected at random from the book. The probability that at least one of them will solve the problem is

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

Choose the correct answer from the options given below :

'A' speaks the truth in 80% of the cases while 'B' in 90% of the cases. The probability that they contradict each other in stating the same statement is