Answer:
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.
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