Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E)

Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32

If P (A) = 0.8, P (B) = 0.5 and P (B|A) = 0.4, find

(i) P(A ∩ B) (ii) P(A|B) (iii) P(A ∪ B)

Evaluate P(A ∪ B), if 2P(A) = P(B) = 5/13 and P(A|B) = 2/5.

If P(A) = 6/11 , P(B) = 5/11 and P(A ∪ B) = 7/11, find

(i) P(A∩B) (ii) P(A|B) (iii) P(B|A)

A coin is tossed three times, where

(i) E : head on third toss, F : heads on first two tosses

(ii) E : at least two heads, F : at most two heads

(iii) E : at most two tails, F : at least one tail

Determine P(E|F)

Two coins are tossed once, where

(i) E : tail appears on one coin, F : one coin shows head

(ii) E : no tail appears, F : no head appears

Determine P(E|F)

A die is thrown three times,

E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses

Determine P(E|F)

Mother, father and son line up at random for a family picture

E : son on one end, F : father in middle

Determine P(E|F)

A black and a red dice are rolled.

(a) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

(b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

A fair die is rolled. Consider events E = {1,3,5}, F = {2,3} and G = {2,3,4,5}

Find

(i) P(E|F) and P(F|E)

(ii) P(E|G) and P(G|E)

(iii) P((E ∪ F)|G) and P ((E ∩ F)|G)

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl?

An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.

If P (A) = 1/2, P(B) = 0, then P (A|B) is

If A and B are events such that P(A|B) = P(B|A), then