Probability that the birth weight of a baby will exceed 8 lb

Probability that the birth weight of a baby will exceed 8 lbs is .27. The probability that the length, at birth, will exceed 20 inches is .33. The probability that a baby will either be above 8 lbs or exceed 22 inches, at birth, is .39. What is the probability that the baby will be both above 8 lbs and exceed 20 inches?

Solution

Let A be the event that the birth weight of a baby will exceed 8 lbs

Let B be the event that the length at birth of a baby will exceed 20 inches

Then,P(A)=0.27

P(B)=0.33

P(A union B)=0.39

Then required probability, P(A intersection B)=P(A)+P(B)-P(A union B)=0.27+0.33-0.39=0.21