Archie is stranded in a war zone in the land of the Xhosas. His only chance of s

Question

Archie is stranded in a war zone in the land of the Xhosas. His only chance of survival is to reach Sudland, which lies 100 miles away. There are just two routes to Sudland; one is through a desert, and the other is a long and perilous trek through the mountains. Both routes are terribly dangerous. In the past, 47% of all who tried to reach Sudland failed. Of all attempts to reach Sudand, 11 out of every 18 were by the desert route. Although it is the longer route, the mountains seem to provide more success: 64% of those who attempted to reach Sudland through the mountains were successful. To save time, Archie intends to go via the desert. What are his chances of making it through to Sudland? Round your answer to two decimal places. (If necessary, consult a list of formulas.)

Explanation / Answer

Pr(Sudland reaching failure) = 0.47

Pr(Sudland reaching success) = 1 - 0.47 = 0.53

Pr(Desert route follower) = 11/18

Pr(Sudland Route Follower) = 1 - 11/18 = 7/18

Pr(Mountain route success) = 0.64

Pr(Sundland Success) = Pr(Desert route success) * Pr(People folllows desert route) + Pr(Mountain route success) * Pr(People follows mountain route)

0.53 = 11/18 * p + 0.64 * 7/18

11/18 * p = 0.28111

p = 0.46

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