A true-false question is to be posed to a husband and wife team. Both the husband and the wife will give the correct answer with probability 0.8. Which of the following is a better strategy for the couple? Strategy 1: choose one of them at random and ask the chosen person to answer the question Strategy 2: have them both answer the question. If their answers agree, give the common answer; if they disagree, flip a fair coin to determine which answer to given.

Question

Mathematics

Genesis

16 June, 03:14

A true-false question is to be posed to a husband and wife team. Both the husband and the wife will give the correct answer with probability 0.8. Which of the following is a better strategy for the couple? Strategy 1: choose one of them at random and ask the chosen person to answer the question Strategy 2: have them both answer the question. If their answers agree, give the common answer; if they disagree, flip a fair coin to determine which answer to given.

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Answers (1)

Know the Answer?

Mariana Montgomery · Answer 1

Choose either strategy both are equally successful

Step-by-step explanation:

Given:-

- The probability of success for both husband (H) and wife (W) are:

P (W) = 0.8, P (H) = 0.8

Find:-

- Which of the following is a better strategy for the couple?

Solution:-

Strategy 1

- First note that P (W) & P (H) are independent from one another, i. e the probability of giving correct answer of husband does not influences that of wife's.

- This strategy poses an event such that either wife knows the answer and answer it correctly or the husband knows and answers in correctly.

- We will assume that probability of either the husband or wife knowing the answer is 0.5 and the two events of knowing and answering correctly are independent. So,

P (Wk) = P (Hk) = 0.5

- The event P (S1) is:

P (S1) = P (Hk & H) + P (Wk & W)

P (S1) = 0.5*0.8 + 0.5*0.8

P (S1) = 0.8

- Hence, the probability of success for strategy 1 is = 0.8

Strategy 2

- Both agree, then the common answer is selected otherwise, one of their answers is chosen at random.

- The success of strategy 2, will occur when both agree and are correct, wife is correct and answers while husband is not or husband is correct and he answers.

- The event P (S2) is:

P (S2) = P (H & W) + P (H / W' & Hk) + P (H' / W & Wk)

P (S2) = P (H & W) + P (H / W') P (Hk) + P (H' / W) P (Wk)

P (S2) = P (H & W) + P (H / W') * 0.5 + P (H' / W) * 0.5

P (S2) = 0.5 * [ P (H & W) + P (H / W') ] + 0.5 * [ P (H' / W) + P (H & W) ]

P (S2) = 0.5*P (H) + 0.5*P (W)

P (S2) = 0.5*0.8 + 0.5*0.8

P (S2) = 0.8

- Hence, the probability of success for strategy 2 is = 0.8

Both strategy give us the same probability of success.