A scientist has to choose a route out of the 5 routes to come out of the rain fo

Question

A scientist has to choose a route out of the 5 routes to come out of the rain forest in an hour The probability of the success by choosing the first route is 0.6. the second route is-0.3. the third route -0.2. the forth route -0.1 and the fifth route -0.1. If the scientist came out of the forest in an hour. (please explain your answers) 1. a. What is the probability that he has chosen the first rout? b. is it beneficial to choose one of these routes? (Mathematical proof of your claim is required)

Explanation / Answer

assume that all routes are equally likely to be selected
X - come out of forest
P(1|X) = P(1 and X) /P(X)
P(X) = P(X|1)P(1) + ... P(X|5)P(5)
= 1/5 ( 0.6 + 0.3 + 0.2 +0.1 +0.1)
= 1/5 (1.3)

P(1 and X) = 0.6 /5
hence required probability = 0.6/1.3 = 6/13

b)
P( 1 and X)= 0.6/5 which is greater than P(i and X) for i = 2,3,4,5

hence selecting first route is beneficial

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