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 is married.
express the probability as a simplified fraction
the probability is
(type an integer or a simplified fraction)

Explanation:

Step1: Recall the formula for conditional probability

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 male and \(B\) is the event that the person is married, then \(P(A\cap B)\) is the number of married - males and \(P(B)\) is the total number of married people.

Step2: Identify the relevant values from the table

The number of married - males (\(A\cap B\)) is \(70\) (from the cell where the "Male" row and "Married" column intersect). The total number of married people (\(B\)) is \(142\) (from the "Total" row and "Married" column).

Step3: Calculate the fraction

Using the formula \(P(A|B)=\frac{n(A\cap B)}{n(B)}\), we substitute \(n(A\cap B) = 70\) and \(n(B)=142\). So, \(P=\frac{70}{142}\). Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The GCD of \(70\) and \(142\) is \(2\). So, \(\frac{70\div2}{142\div2}=\frac{35}{71}\).

Answer:

\(\frac{35}{71}\)