Question

. 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? 19. What is the probability the professor takes his bike and is late? 20. What is the probability the professor takes his bike or is late? 21. If the professor is late, what is the probability he rode his bike? 22. Are the events taking the bike and being late independent? Why or why not? 23. Are the events taking the bike and being late exclusive? Why or why not?

Answer 1

Let B shows the event that professor rides his bike and C shows the event that professor rides his car. So we have

P(B) = 0.80, P(C) = 0.20

Let L shows the event that professor is late so

P(L|B) = 0.10, P(L|C) = 0.05

18:

By the law of total probability, the probability the professor is late will be

P(L) = P(L|B)P(B) + P(L|C)P(C) = 0.10 * 0.80 + 0.05 * 0.20 = 0.08 + 0.01 = 0.09

Answer: 0.09

19:

The required probability is

P(L and B) = P(L|B)P(B) = 0.10 * .80 = 0.08

Answer: 0.08

20:

The required probability is

P(L or B) = P(L) +P(B) - P(L and B) = 0.09 + 0.80 - 0.08 = 0.81

Answer: 0.81

21:

P(B |L) = P(L and B) / P(L) = 0.08 / 0.09 = 0.8889

Answer: 0.8889

22:

No because P(L|B) is not equal to P(L).

23:

No because P(L and B) is not equal to zero.