A company has just received new machinery that must be installed and checked bef

Question

A company has just received new machinery that must be installed and checked before it becomes op erational. The accompanying table shows a manager's probability assessment for the number of days required before the machinery becomes operational. Number of Days34567 Probability 0.08 0.20 0.41 0.24 0.07 Let A be the event "It will be more than 4 days before the machinery becomes operational," and let B be the event It will be less than 6 days before the machinery becomes operational." a) find the probability of event A b) find the probability of event B c) find the probability of the complement of event A d) find the probability of the intersection of events A and B e) find the probability of the union of events A and B

Explanation / Answer

a)P(A)=P(X>4) =P(X=5)+P(X=6)+P(X=7)=0.41+0.24+0.07=0.72

b)P(B)=P(X<6)=P(X=3)+P(X=4)+P(X=5)=0.08+0.20+0.41=0.69

c)P(Ac)=1-P(A)=1-0.72=0.28

d)P(A n B)=P(X=5)=0.41

e) P(A u B)=P(A)+P(B)-P(A n B)=0.72+0.69-0.41=1

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