4.67 Two men each tossing a balanced coin obtain a

“match” if both coins are heads or if both are tails. The process is repeated three times.

a What is the probability of three matches?

b What is the probability that all six tosses

(three for each man) result in “tails”?

c Coin tossing provides a model for many practical experiments. Suppose the “coin tosses”

represented the answers given by two students to three specific true-false questions on an examination. If the two students gave three matches for answers, would the low probability determined in part

(a) suggest collusion?