Suppose that 5 years of service, 30% of computers have problems with motherboards (MB), 40% have problems with hard drives (HD) and 15% have problems with both MB and HD. What is the probability that a 5-year old computer still has fully functioning MB and HD

0.45

Explanation:

Probability of bad motherboard(MB) = 0.30

Probability of bad hard-drive(H) = 0.40

Probability of bad motherboard and hard-drive (MB and H) = 0.15

P(MB U H)= P(MB) + P(H) -P(MB and H)

=0.30+0.40-0.15=0.55

Probability that a 5 year old computer would have no problems of motherboard and hard-drive =

1-P(MB U H) = 1-0.55= 0.45