You read about a survey in the newspaper, which says the following: ”If you’re d

Question

You read about a survey in the newspaper, which says the
following: ”If you’re driving a compact car, the probability you survive the
collision with a sport car is 0.9, and the probability you survive the collision
with an SUV is 0.85. If you’re driving a sport car the probability you survive
a collision with a compact car is 0.8 and the the probability you survive a
collision with a SUV is 0.7. If you’re driving an SUV the probability you
survive a collision with a compact car is 0.95, and the collision with a sport
car is 0.9. Whatever, you’re driving the probability you survive a crash with
a car of the same type (compact, sport or SUV) is 0.8”
You just moved into a new city in which 20% of cars are compact, 20% of
cars are sport cars and 60% of cars are SUVs, and you want a buy a car
to use it in the city. What car would you buy to maximize the chance of
surviving in a collision (assume that collision of any pair of cars has the
same probability).

Explanation / Answer

P(survival) = Sumof (probability of survival of collision with a particular type of car x proportion of that type of car)

P(surving a collision while driving a compact car) = 0.8x0.2 + 0.9x0.2 + 0.85x0.6 = 0.85

P(surving a collision while driving a sports car) = 0.8x0.2 + 0.8x0.2 + 0.7x0.6 = 0.74

P(surving a collision while driving an SUV) = 0.95x0.2 + 0.9x0.2 + 0.8x0.6 = 0.85

A compact car or an SUV can be brought to maximize the chance of surviving a collision as both of these vehicles have same probability of survival.

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