Question

according to a research agency, in 31% of marriages the woman has a bachelors degree and the marriage lasts at least 20 years. according to a census report, 41% of women have a bachelors degree what is the probability a randomly selected marriage will last at least 20 years if the woman has a bachelors degree? note: 52% of all marriages last at least 20 years

the probability that a randomly selected marriage will last at least 20 years if the woman has a bachelors degree is
(round to three decimal places as needed)

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Let \(A\) be the event that the marriage lasts at least 20 years and \(B\) be the event that the woman has a bachelor's degree. We are given that \(P(A\cap B) = 0.31\) (the probability that the woman has a bachelor's degree and the marriage lasts at least 20 years) and \(P(B)=0.41\) (the probability that the woman has a bachelor's degree).

Step2: Substitute the values into the formula

Substitute \(P(A\cap B) = 0.31\) and \(P(B)=0.41\) into the formula \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). So \(P(A|B)=\frac{0.31}{0.41}\).

Step3: Calculate the value

\(\frac{0.31}{0.41}\approx0.756\)

Answer:

\(0.756\)