According to a recent report 66 7% of men and 50 1% of women in the United State

Question

According to a recent report 66 7% of men and 50 1% of women in the United States were over find the probability that a randomly selected American fits the following description (a) An overweight man (b) Overweight (c) Are the events that an adult is a man and that an adult is overweight independent? Explain eight Given that 487% of Americans are men and 513% are women (a) The probability that a randomly selected adult is an overweight man is (Type an integer or decimal rounded to three decimal places as needed)

Explanation / Answer

Here,

Pr(Men) = 48.7% = 0.487

Pr(Women) = 51.3% = 0.513

Pr(Overweight l men) = 66.7% = 0.667

Pr(Overweight l women) = 50.1% = 0.501

(a) Pr(Overweight man ) = Pr(Overweight l men) * Pr(Men) = 0.667 * 0.487 = 0.325

(b) Pr(Overweight) =  Pr(Overweight l men) * Pr(Men) + Pr(Overweight l women) * Pr(women)

= 0.667 * 0.487 + 0.501 * 0.513 = 0.582

(c) Two events A and B would be independet if

P(A and B) = P(A) * P(B)

P(Men and overweight) = 0.325

Pr(Overweight) * Pr(men) = 0.582 * 0.487 = 0.2834

so not similar, so these two events are not independent.

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