There are two routes to the summit of Mt. Aspiring. The North West Ridge is not

Question

There are two routes to the summit of Mt. Aspiring. The North West Ridge is not very difficult by mountaineering standards, and so there is a probability of 0.76 of successfully reaching the top by this route. The South West Ridge is much more technically demanding, is recommended only for experienced climbers, and there is a probability of 0.39 of reaching the summit by this route. Guides have determined that 62% of climbers will take the North West Ridge route, and 38% will take the South West Ridge route. Give your answers to 3 places past the decimal point. a) What is the probability that a randomly chosen climber uses the South West Ridge route and reaches the summit? Submit Answer Tries 0/2 b) What is the probability that a randomly chosen climber of unknown skill and route will reach the summit? Submit Answer Tries 0/2 c) Two Canadian climbers Pierre and Colleen successfully reach the summit, only to find a satisfied climber, Tenzing, there before them. Conditions were icy so they couldn't see any tracks from this climber. What is the probability that Tenzing used the more difficult South West Ridge route? Submit Answer Tries 0/2

Explanation / Answer

Q 1

a) Let A be the event that the randomly chosen climber reaches the summit, and

let SW be the event that he uses the South West Ridge route

P(A|SW) = 0.39

P(SW) = 0.38

P(that randomly chosen climber uses the South West Ridge route and reaches the summit) = P(A|SW)*P(SW) = 0.39*0.38 = 0.148

b)

P(A) = P(that randomly chosen climber uses the South West Ridge route and reaches the summit) +

P(that randomly chosen climber uses the North West Ridge route and reaches the summit)

= 0.39*0.38+ 0.76*0.62 = 0.1482+0.4712 = 0.619

c)

P(climber used South West Ridge Route | climber reaches Summit)

= P(climber used South West Ridge Route and reaches Summit) / P(climber reaches Summit)

= 0.1482/0.6194

= 0.239

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