Answer:
(a) The probability that a randomly selected adult is either overweight or obese is 0.569.
(b) The probability that a randomly selected adult is neither overweight nor obese is 0.431.
Step-by-step explanation:
Let <em>A</em> = a person is over weight and <em>B</em> = a person is obese.
The information provided is:
An adult is considered overweight if the BMI ≥ 25 but BMI < 30.
An obese adult will have a BMI ≥ 30.
According to the range of BMI the events A and B are independent.
P (A) = 0.331 and P (B) = 0.357.
(a)
Compute the probability that a randomly selected adult is either overweight or obese as follows:
P (A ∪ B) = P (A) + P (B) - P (A ∩ B)
= P (A) + P (B) - P (A)×P (B)
Thus, the probability that a randomly selected adult is either overweight or obese is 0.569.
(b)
Compute the probability that a randomly selected adult is neither overweight nor obese as follows:
Thus, the probability that a randomly selected adult is neither overweight nor obese is 0.431.