Reference no: EM13307556

1. A fair coin is tossed three times and it is recorded whether it falls head or tail.

(a) Give the sample space S for the experiment.

(b) Consider the following events: E = a head on the first toss; F = a head on the second toss; G = a head on the third toss. Give the subset of outcomes in S that defines each of the events E, F and G.

(c) Describe the following events in terms of E, F and G and find the probabilities for the events.

• getting a head on the first toss and a head on the second toss.
• getting a head on the first toss or a head on the second toss.
• getting a tail on the first toss.
• getting at least one head in the three tosses.

(d) Are E and F mutually exclusive events? Give a reason for your answer.

2.

Three unusual dice, A, B, and C are constructed such that die A has the numbers 3, 3, 4, 4, 8, 8; die B has the numbers 1, 1, 5, 5, 9, 9; and die C the numbers 2, 2, 6, 6, 7, 7.

(a) If dice A and B are rolled, find the probability that B beats A, that is, that the number that appears on die B is greater than the number on die A.

(b) If dice B and C are rolled, find the probability that C beats B.

(c) If dice A and C are rolled, find the probability that A beats C.

(d) Which die is the best of the three? Explain your answer.

Attachment:- MATH_Question.pdf