Question

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

	married	never married	divorced	widowed	total
female	62	38	17	10	127
total	122	75	31	13	241

express the probability as a simplified fraction.
the probability is . (type an integer or a simplified fraction.)
express the probability as a decimal.
the probability is approximately . (round to two decimal places as needed.)

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 $0.49$.