A1 be the event that the receiver functions properly throughout the warranty period, A2 be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P (A1) 5.95, P (A2) 5.98, and P (A3) 5.80. a. What is the probability that all three components function properly throughout the warranty period

Question

Cherish Conner

Mathematics

21 September, 22:47

A1 be the event that the receiver functions properly throughout the warranty period, A2 be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P (A1) 5.95, P (A2) 5.98, and P (A3) 5.80. a. What is the probability that all three components function properly throughout the warranty period

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Felicity Kirby · Answer 1

0.7448

Step-by-step explanation:

P (A1) = 0.95

P (A2) = 0.98

P (A3) = 0.8

We have to find P (all three components function properly) = P (A1∩A2∩A3).

We know that the these three events are independent so,

P (all three components function properly) = P (A1∩A2∩A3) = P (A1) * P (A2) * P (A3)

P (all three components function properly) = P (A1∩A2∩A3) = 0.95*0.98*0.80

P (all three components function properly) = P (A1∩A2∩A3) = 0.7448