Question

According to some internet research, 85.2% of adult Americans have some form of medical insurance, and 75.9% of adult Americans have some form of dental insurance. If 89.4% of adult Americans have either medical or dental insurance, then what is the probability that a randomly selected adult American with have both medical and dental insurance

Answer 1

Answer:

0.717 or 71.7%

Step-by-step explanation:

P(M) = 0.852

P(D) = 0.759

P(M or D) = 0.894

The probability that a randomly selected American has both medical and dental insurance is given by the probability of having medical insurance, added to the probability of having dental insurance, minus the probability of having either insurance:

$P(M\ and\ D) = P(M)+P(D)-P(M\ or\ D)\\P(M\ and\ D) =0.852+0.759-0.894\\P(M\ and\ D) =0.717=71.7\%$

The probability is 0.717 or 71.7%.