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, 48% of all who tried to reach Sudland failed. Of all attempts to reach Sudland, 22 out of every 30 were by the desert route. Although it is the longer route, the mountains seem to provide more success: 74% 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.

I think this is Bayes Theorem. Please list STEPS, I keep getting the same problem with different variables. I really want to know how to solve this problem, and others like it.

GIVEN:

48% of all who tried FAILED

22 out of every 30 (of all attempts) took desert route

74% Mountain Route SUCCESSFUL

Archie goes desert route. What are his chances of success?

Round your answer to two decimal places.

Question #2 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 48% all of who tried to reach Sudland failed. Of a attempts to reach Sudland, 22 out of every 30 were by the desert route. Although it is the longer route, the mountains seem to provide more success 74% 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.) Clear Undo Help

Explanation / Answer

let probabilty of failure =P(F)=0.48

and probabilty of success =P(S)=1-0.48=0.52

also probabilty to go through desert =P(D)

and through mountain =P(M)

probabilty of failure =P(F) =P(D)*P(F|D) +P(M)*P(F|M)

0.48 =(22/30)*P(F|D) +(8/30)*0.26

P(F|D) =0.56

hence probabilty of being successful given goes through desert =P(S|D) =1-P(F|D)=1-0.56=0.44

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