4. Suppose that a student goes to class by bus, by car, or on foot for the 60%,

Question

4. Suppose that a student goes to class by bus, by car, or on foot for the 60%, 15%, and 25% of the time respectively. The probability that they are late to class depends on their means of transportation. If they take the bus, they have a 5% chance of being late; if they go by car, they have an 20% chance of being late, and the overall probability that they are late is 0.065. (a) What is the probability that they will be late given that they walk to class? (1.5 points) (b) What is the probability that they walked to class given that they are late? (1 point)

Explanation / Answer

P(B) = 0.6, P(C) = 0.15 and P(F) = 0.25
P(L|B) = 0.05, P(L|C) = 0.2

P(L) = 0.065

a)
P(L) = P(L|B)*P(B) + P(L|C)*P(C) + P(L|F)*P(F)

0.065 = 0.05*0.6 + 0.2*0.15 + P(L|F)*0.25

P(L|F)*0.25 = 0.065 - 0.06

P(L|F) = 0.005/0.25 = 0.02

b)
P(F|L) = P(L|F)*P(F)/P(L)
= 0.02*0.25/0.065
= 0.0769

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