Question

3. According to the U.S. census website (www.census.gov), based on the U.S. population in 2010, the probability that a randomly selected man is 65 or older is 0.114,

and the probability that a randomly selected woman is 65 or older is 0.146. In the questions that follow, round your answers to the nearest thousandth:
a. If a man is selected at random and a woman is selected at random, what is the probability that both people selected are 65 or older?
(Hint: Use the multiplication rule for independent events.)
b. If two men are selected at random, what is the probability that both of them are 65 or older?
c. If two women are selected at random, what is the probability that neither of them is 65 or older?

Answer 1

a. 0.017

b. 0.013

c. 0.021

Explanation:

Let p be the probability that a randomly selected man is 65 or older

And q be the probability that a randomly selected woman is 65 or older

Then p=0.114 and q=0.146

Using the multiplication rule for independent events:

a. If a man is selected at random and a woman is selected at random, the probability that both people selected are 65 or older is p × q = 0.114 × 0.146 ≈ 0.017

b. If two men are selected at random, the probability that both of them are 65 or older is p × p = 0.114 × 0.114 ≈ 0.013

c. If two women are selected at random, the probability that neither of them is 65 or older is q × q = 0.146 × 0.146 ≈ 0.021