express the following probability as a simplified fraction and as a decimal. if one person is selected from…
express the following probability as a simplified fraction and as a decimal. if one person is selected from the population described in the table, find the probability that the person is male, given that this person never married. marital status of a certain population, ages 18 or older, in millions\n| | married | never married | divorced | widowed | total |\n|--|--|--|--|--|--|\n| male | 60 | 37 | 14 | 3 | 114 |\n| female | 62 | 38 | 17 | 10 | 127 |\n| total | 122 | 75 | 31 | 13 | 241 |\nexpress the probability as a simplified fraction.\nthe probability is . (type an integer or a simplified fraction.)\nexpress the probability as a decimal.\nthe probability is approximately . (round to two decimal places as needed.)
Answer
Explanation:
Step1: Recall conditional - probability formula
The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of the table, if $A$ is the event that the person is male and $B$ is the event that the person is never - married, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in the intersection of $A$ and $B$, and $n(B)$ is the number of elements in $B$.
Step2: Identify $n(A\cap B)$ and $n(B)$ from the table
The number of never - married males $n(A\cap B) = 37$. The number of never - married people $n(B)=75$.
Step3: Calculate the probability as a fraction
The probability that the person is male given that the person is never married is $P=\frac{37}{75}$.
Step4: Calculate the probability as a decimal
$37\div75\approx0.49$.
Answer:
The probability as a simplified fraction is $\frac{37}{75}$. The probability as a decimal is approximately $0.49$.