Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and the CD player. Let A₁ be the event that the receiver functions properly throughout the warranty period, A₂ be the event that the speaker functions properly throughout the warranty period, and A₃ be the event that the the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with

P(A₁) = 0.95

P(A₂) = 0.98

P(A₃) = 0.80

a. What is the probability that all three components function properly throughout the warranty period?

b. What is the probability that at least one component needs service during the warranty period?

c. What is the probability that all three components need service during the warranty period?

d. What is the probability that only the receiver needs service during the warranty period?

e. What is the probability that exactly one of the three components needs service during the warranty period?

f. What is the probability that all three components function properly throughout the warranty period but that at least one fails within a month after the warranty expires?

Show me a vann diagram and all the necessary steps and details from scratch as much as possible please. Thank you.