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Probability : What is the best strategy?

18. A true-false question is to be posed to a husband and wife team on a quiz show. Both the husband and the wife will, independently, give the correct answer with probability p. which of the following is a better strategy for the couple?
(a) Choose one of them and let that person answer the question; or
(b) have them both consider the question and then either give the common answer if they agree or, if they disagree, flip a coin to determine which answer to give?


Solution Preview

a. We may choose the wife or husband. Lets assume that the probability of choosing the husband is "h" and probability of choosing the wife is "1-h"

The probability of giving the right answer is p and giving the wrong answer is 1-p . Thus we may have 4 different results. The probability of their combination would be equal to the multiplication of their probabilities.

1. We choose the husband and he ...

Solution Summary

Strategies involving a true-false question are investigated in terms of probability. The solution is detailed and well presented.