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, 26% of all who tried to reach Sudland failed. Of all attempts to reach Sudland, 1 out of every 40 were by the desert route. Although it is the longer route, the mountains seem to provide more success: 75% 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

Answer 1

Answer:

The  chances of success for Archie is $P(S|D) = 35\%$

Step-by-step explanation:

From the question we are told that

 The distance of Sudland from Xhosas is   d =  100 miles

  The probability  of failure is  $P(F) = 0.26$

  The probability of choosing the desert route is   $P(D) = \frac{1}{40} = 0.025$

The probability of reaching Sudland through the mountain is  $P(S|M) =0.75$

Generally the probability of choosing the  mountains route is

         $P(M) = 1 - P(D)$

           $P(M) = 1 - 0.025$

             $P(M) = 0.975$

Generally the probability of success is mathematically represented as

       $P(S) = 1- P(F)$

         $P(S) = 1- 0.26$

          $P(S) = 0.74$

       

Generally the probability of success in reaching Sudland is also mathematically represented as

     $P(S) = P(S|M) * P(M) + P(S|D) * P(D)$

=>   $P(S|D) = \frac{P(S) - P(S|M) * P(M)}{P(D)}$

substituting values

=>  $P(S|D) = \frac{0.74 - 0.75 * 0.975}{0.025}$  

=>  $P(S|D) = 0.35$  

=>  $P(S|D) = 35\%$