1. 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) 2. Compute P(A|B), if P(B) = 0.5 and P (A B) = 0.32 3. 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) 4. Evaluate P(A B), if 2P(A) = P(B) = 5 13 and P(A|B) = 2 5 5. If P(A) = 6 11 , P(B) = 5 11 and P(A B) 7 11 , find (i) P(AB) (ii) P(A|B) (iii) P(B|A) Determine P(E|F) in Exercises 6 to 9. 6. 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 o 7. 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 8. A die is thrown th
Question 1: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)
Question 2:Compute P(A|B), if P(B) = 0.5 and P (A B) = 0.32
Question 3: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)
Question 4:Evaluate P(A B), if 2P(A) = P(B) = 5 13 and P(A|B) = 2 5
Question 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) Determine P(E|F) in Exercises 6 to 9
Question 6: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 o
Question 7: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
Question 8:A die is thrown three times, E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses
Question 9:Mother, father and son line up at random for a family picture E : son on one end, F : father in middle
Question 10: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.
Question 11: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)
Question 12: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?
Question 13: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?
Question 14: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’.
Question 15: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’. In each of the Exercises 16 and 17 choose the correct answer:
Question 16:If P(A) = 1 2 , P (B) = 0, then P(A|B) is (A) 0 (B) 1 2 (C) not defined (D) 1
Question 17:If A and B are events such that P(A|B) = P(B|A), then (A) A B but A B (B) A = B (C) A B = (D) P(A) = P(B)
