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Probability. A professor rides his bike to work some days and drives his car on the other days. On any day there is an 80% chance the professor will ride his bike and a 20% chance he will take his car. If the professor rides his bike, there is a 10% chance he will be late. If he takes his car, theres a 5% chance he will be late. 18. What is the probability the professor is late

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Answer:

0.09

Step-by-step explanation:

Given :

P(bike) = 0.8

P(car) = 0.2

P(Late given car) = P(Late | car) = 0.05

P(Late given bike) = p(Late | bike) = 0.1

Probability that professor is late :

P(late) = [P(Late | car) * p(car)] + [p(Late | bike) * p(bike)]

P(late) = [0.05 * 0.2] + [0.1 * 0.8]

P(late) = 0.01 + 0.08

P(late) = 0.09

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