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Statistics:

MUST SHOW REASONING AND PROPER STEPS.

1.A. 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 0.84 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 0.28 of reaching the summit by this route. Guides have determined that 76% of climbers will take the North West Ridge route, and 24% will take the South West Ridge route. Give your answers to 3 places past the decimal point. What is the probability that a randomly chosen climber uses the South West Ridge route and reaches the summit? What is the probability that a randomly chosen climber of unknown skill and route will reach the summit? 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? 1.B. The probability that a randomly chosen Nova Scotian male hunts is 0.23, and the probability that they drive an all terrain vehicle (ATV) is 0.46. The probability that they do both is 0.15. Must show proper reasoning and steps. Are the events hunt" and drive an ATV" disjoint (mutually exclusive)? Are the events hunt" and drive an ATV" independent? Find the probability that a randomly chosen Nova Scotian male hunts or drives an ATV. Give your answer to two places past the decimal. Find the probability that a randomly chosen Nova Scotian male drives an ATV if he hunts. Give your answer to 3 places past the decimal

Explanation / Answer

1A. P(Randomly chosen climber using the south west ridge route and reaches the summit)

= P(A climber is using south west ridge route)*P( reaching the summit using south- west ridge route) [As both the cases are independent ]

= (24/100)*0.28

= 0.0672

= 0.067 (Approx.)

P(A randomly chosen climber of unknown skill and route will reach the summit)

= P(A climber takes south west route and reach the summit) + P(A climber takes a north west route and reach the summit)

= P(A climber takes south west route) P(climber reaches the summit using south-west route) +

P(A climber takes north west route) P(climber reaches the summit using north-west route)

= (24/100)*0.28 + (76/100)*0.84

= .7056

= .706 (Approx.)

For the part 3. we have to use Baye's Theorem

P(Tenzing uses more difficult path (i.e. South-West route) | Tenzing reaches the summit)

= { P(Tenzing reaches the summit | Tenzing uses south west route) * P(Tenzing uses south west route) } / {P(Tenzing reaches the summit | Tenzing uses south west route) * P(Tenzing uses south west route) + P(Tenzing reaches the summit | Tenzing uses north west route) * P(Tenzing uses north west route) }

= ( 0.24*0.28 ) / (0.24*0.28 + 0.76*0.84 )

= 0.095 (Approx.)

[ Chegg guidelines do not recommend me to answer more than one question at a time ]

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