Problem #5 (15 points) Suppose that Jenny has two problems to tasks to finish be

Question

Problem #5 (15 points) Suppose that Jenny has two problems to tasks to finish before the end of the day: laundry and cleaning the room. The probability that she finishes will do the laundry before the end of the day is 0.5, the probability that she will clean the room before the end of the day is 0.4. The probability that she finishes both tasks by the end of the day is 0.15. a) (3 points) Find the probability that the finishes at least one task by the end of the day? b) (3 points) Find the probability that the will finish exactly one of these two tasks? e) (3 points) Find the probability that she will only be able to clean the room, but not do the laundry d) (3 points) Given that she finished the laundry, find the probability that she will be able to finish cleaning the room? (3 points) Are these events independent? e)

Explanation / Answer

a) P(Atleast one task) = P(Laundry) + P(Cleaning room) - P(Both) = 0.5 + 0.4 - 0.15 = 0.75

b) P(Exactly one of the tasks) = P(Atleast one task) - P(Both) = 0.75 - 0.15 = 0.60

c) P(Clean the room but not laundry) = P(Cleaning room) - P(Both) = 0.4 - 0.15 = 0.25

d) P(Cleaning room | Laundry) = P(Both) / P(Laundry) = 0.15/0.50 = 0.30

e) Since P(Cleaning room | Laundry) is not equal to P(Cleaning room), these events are not independent.

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