Answer:
The chances of success for Archie is [tex]P(S|D) = 35\%[/tex]
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 [tex]P(F) = 0.26[/tex]
The probability of choosing the desert route is [tex]P(D) = \frac{1}{40} = 0.025[/tex]
The probability of reaching Sudland through the mountain is [tex]P(S|M) =0.75[/tex]
Generally the probability of choosing the mountains route is
[tex]P(M) = 1 - P(D)[/tex]
[tex]P(M) = 1 - 0.025[/tex]
[tex]P(M) = 0.975[/tex]
Generally the probability of success is mathematically represented as
[tex]P(S) = 1- P(F)[/tex]
[tex]P(S) = 1- 0.26[/tex]
[tex]P(S) = 0.74[/tex]
Generally the probability of success in reaching Sudland is also mathematically represented as
[tex]P(S) = P(S|M) * P(M) + P(S|D) * P(D)[/tex]
=> [tex]P(S|D) = \frac{P(S) - P(S|M) * P(M)}{P(D)}[/tex]
substituting values
=> [tex]P(S|D) = \frac{0.74 - 0.75 * 0.975}{0.025}[/tex]
=> [tex]P(S|D) = 0.35 [/tex]
=> [tex]P(S|D) = 35\%[/tex]
