Question

How to find the indicated probability to this problem? This is a homework practice. Show your work. Thanks!

Answer 1

You want to find $P(\text{no exercise}\mid\text{woman})$; that is, given that you randomly choose from the pool of women, the probability that she does not exercise.

By definition of conditional probability,

$P(\text{no exercise}\mid\text{woman})=\dfrac{P(\text{no exercise AND woman})}{P(\text{woman})}$

496 of the total 1026 people are woman, and 341 of the 1026 people are women and do not exercise, so

$P(\text{no exercise}\mid\text{woman})=\dfrac{\frac{341}{1026}}{\frac{496}{1026}}=\dfrac{341}{496}=0.6875\approx0.688$

A simpler way of doing this is to look at what's called the marginal distribution of women in the table. Basically this comes down to ignoring all but the data pertaining to the women. There's a total of 496 women, and 341 of them do not exercise. So the probability that a given woman does not exercise is 341/496.