Assume that there are two types of bikers, those who stop at stop signs and thos
ID: 3236680 • Letter: A
Question
Assume that there are two types of bikers, those who stop at stop signs and those who do not. Of all bikers, 20% are hit by cars. Of those bikers who are hit, 50% didn’t stop at a stop sign. Finally, if you don’t stop at a stop sign you have a 60% chance of getting hit by a car.
a. What is the probability of a bikers having stopped at a stop sign, given that they have been hit by a car?
b. What percentage of all bikers stop at stop signs?
c. What percentage of all bikers stop at stop signs and are not hit by a car?
Explanation / Answer
probability that a biker is hit by a car, P(H) = 0.2
Probability of getting hit and do not stop, P(H and S') = 0.5
Probability that biker hit when stopped and when not stopped, P(H and S) + P(H and S') = 0.6
P(H and S) + P(H and S') = 0.6
P(H and S') = 0.5
P(H and S) = 0.1 (stopped and hit)
(A)
the probability of a bikers having stopped at a stop sign, given that they have been hit by a car,
P(S|H) = P(S and H)/P(H) = 0.1/0.2 = 0.5
(C)
P(S and H') = 1 - P(S and H) = 1 - 0.1 = 0.9
Hence 90% of all bikers stop at stop signs and are not hit by a car.