Question

find the indicated probability. express your answer as a simplified fraction unless otherwise noted. the table below describes the smoking habits of a group of asthma sufferers.

	nonsmoker	light smoker	heavy smoker	total
women	331	71	85	487
total	706	145	112	963

if one of the 963 subjects is randomly selected, find the probability that the person chosen is a woman given that the person is a light smoker. round to the nearest thousandth.
0.849
0.151
0.146
0.490

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of the table, if $A$ is the event that the person is a woman and $B$ is the event that the person is a light - smoker, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of women who are light - smokers and $n(B)$ is the number of light - smokers.

Step2: Identify values from the table

From the table, the number of women who are light - smokers $n(A\cap B) = 71$, and the number of light - smokers $n(B)=145$.

Step3: Calculate the probability

$P(A|B)=\frac{71}{145}\approx0.490$

Answer:

0.490