Question

according to a research agency, in 22% of marriages the woman has a bachelors degree and the marriage lasts at least 20 years. according to a census report, 35% 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: 49% 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: Define events

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 know $P(A\cap B)=0.22$, $P(B) = 0.35$.

Step2: Use conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$.

Step3: Substitute values

Substitute $P(A\cap B) = 0.22$ and $P(B)=0.35$ into the formula: $P(A|B)=\frac{0.22}{0.35}$.

Step4: Calculate the result

$P(A|B)=\frac{0.22}{0.35}\approx0.629$.

Answer:

$0.629$