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 or is divorced. marital status of a certain population, ages 18 or older, in millions

	female	male	total
never married	30	44	74
divorced	17	9	26
widowed	6	2	8
total	116	116	232

the probability that the person is male or is divorced is (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the formula for the probability of the union of two events

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event that the person is male and $B$ be the event that the person is divorced.

Step2: Calculate $P(A)$, $P(B)$ and $P(A\cap B)$

The total number of people is $232$ million. The number of males is $116$ million, so $P(A)=\frac{116}{232}$. The number of divorced people is $26$ million, so $P(B)=\frac{26}{232}$. The number of divorced - males is $9$ million, so $P(A\cap B)=\frac{9}{232}$.

Step3: Substitute into the formula

$P(A\cup B)=\frac{116}{232}+\frac{26}{232}-\frac{9}{232}=\frac{116 + 26-9}{232}=\frac{133}{232}$.

Answer:

$\frac{133}{232}\approx0.573$