Question 1
Among the policyholders of an insurance company, 64% have an auto policy, 42% have a homeowners policy and 27% have both. One policyholder is chosen at random.
Calculate the probability that the policyholder has neither.
General Probability
Write the event in symbols first. At least one is 1 minus none, and a condition changes the denominator: P(A | B) is P(A and B) over P(B).
Question 2
Among the members of a fitness club, 38% have a gym pass, 29% have a pool pass and 12% have both. One member is chosen at random.
Calculate the probability that the member has neither.
Question 3
Of the households in a town, 48% have a streaming service, 35% have a cable package and 16% have both. One household is chosen at random.
Calculate the probability that the household has exactly one of the two.
Question 4
Of the adults surveyed, 62% have a credit card, 41% have a store card and 25% have both. One adult is chosen at random.
Calculate the probability that the adult has exactly one of the two.
Question 5
In a group of insured adults, the proportions with each condition are: high blood pressure 0.24, high cholesterol 0.18, diabetes 0.15. The proportions with two conditions are: high blood pressure and high cholesterol 0.07, high blood pressure and diabetes 0.05, high cholesterol and diabetes 0.04. The proportion with all three is 0.02.
Calculate the probability that a randomly chosen adult has none of the three conditions.