A coin is tossed thrice, and events E and F are defined as:

E : "The first throw results in a head"

F : "The last throw results in tail"

Then, which of the following statements is true for events E and F?

The probability of 'the student knows the answer given that he answered it correctly' is

A die is rolled in such a way that an even number is twice likely to occur as an odd number. If the die is rolled twice, then the mean of the number of perfect squares in two tosses 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 :

The probability distribution of a random variable X is given by

If k > 0, then $P(0 < X \leq 2)$ is equal to

Bag I contains 4 red and 5 black balls, while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be black. Then the probability that it was drawn from Bag II, is

Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be :