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, 16% 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 the events

Let $A$ be the event that the woman has a bachelor's degree and $B$ be the event that the marriage lasts at least 20 years. We are given $P(A\cap B)=0.22$, $P(A) = 0.36$ (not given in the text but assumed for the sake of the problem - if we assume a typo and it should be used in the formula, if not, the problem is incomplete as we need the probability of the woman having a bachelor's degree), and $P(B)=0.49$. We want to find $P(B|A)$.

Step2: Apply the formula for conditional probability

The formula for conditional probability is $P(B|A)=\frac{P(A\cap B)}{P(A)}$.
Substitute the given values: $P(B|A)=\frac{0.22}{0.36}\approx 0.611$.

Answer:

$0.611$