Question

Suppose a researcher determined that 49.3

49.3% of people 18–34 years old in the United States are men. She also finds that, among all Americans 18–34 years old, 17.1

17.1% are men and live at home with their parents, whereas 14.9

14.9% are women and live at home with their parents.

Label each branch of the following tree diagram with the correct probability value.

Answer 1

$P(men) = 0.493 \\ P(women) = 1 -P(men) \\ = 1 -0.493 \\ = 0.507$

P(men and live at home with their parents) = P(men $\cap$ live at home with their parents) = 0.171

P(women and live at home with their parents) = P(women $\cap$ live at home with their parents) = 0.149

P(live at home with their parents | men) $= \frac{0.171}{0.493} = 0.347$

P(other arrangement | men) $= 1 -0.347 = 0.653$

P(live at home with their parents | women) $= \frac{0.149}{0.507} = 0.294$

P(other arrangement | women) $= 1 -0.294 = 0.706$