A die marked 1,2,3 in red and 4,5,6 in green is tossed. Let A be the event that “number is even” and B be the event that “number is marked red”. Find whether the events A and B are independent or not.

Coloured balls are distributed in three bags as shown in the following table:

A bag is selected at random, and then two balls are randomly drawn from the selected bag. They happen to be black and red. What is the probability that they came from the bag I?

If A and B are two independent events such that P(A’ ∩ B) = 2/15 and P(A ∩ B’) = 1/6 then find P(A) and P(B).

State True or False for the statements in the Exercise.

If A and B are two independent events then P(A and B) = P(A).P(B)

State True or False for the statements in the Exercise.

If A and B are mutually exclusive events, then they will be independent also.

State True or False for the statements in the Exercise.

If A and B are independent, then

P (exactly one of A, B occurs) = P(A)P(B′)+P(B) P(A′)

State True or False for the statements in the Exercise.

If A and B are independent events, then P(A′ ∪ B) = 1 – P (A) P(B′)

State True or False for the statements in the Exercise.

Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.

Prove that if E and F are independent events, then the events E and F are also independent.

State True or False for the statements in the Exercise.

Two independent events are always mutually exclusive.