find the indicated probability. express your answer as a simplified fraction unless otherwise noted. the…
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. \n| | nonsmoker | light smoker | heavy smoker | total |\n|--|--|--|--|--|\n| men | 375 | 74 | 27 | 476 |\n| women | 331 | 71 | 85 | 487 |\n| total | 706 | 145 | 112 | 963 |\nif 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.\n0.849\n0.151\n0.146\n0.490
Answer
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