Prompt: According to a survey, only 43% of Americans have a net worth above \$20,000. This varies by age. Out of Americans below the age of 35, only 37% have a net worth above \$20,000. Where as 52% of Americans over the age of 35 have a net worth above \$20,000.
Question: If I pick one person under 35, and another over the age of 35, given that only one of them has a net worth above \$20,000, what is the probability it is the older person?
I see that it is a conditional probability question.
If we let $P(A)$ = over the age of 35 (however it is not stated that half of people are under 35 and the other half are over 35 so this is also confusing).
and $P(B)$ = one of the two has a net worth over \$20,000
then the solution would be $P(A|B)$, but how can I find $P(B)$?
You are setting this up wrong. We know that one person is under $35$ and the other is over $35$. This is not a matter of probability.
Let $A$ be the event that the younger person's net worth is over $\$20000$ and let $B$ be the event that the older person's net worth is over $\$20000$. We are given that exactly one of these events occurs, that is $(A\cap \overline{B})\cup(\overline{A}\cap B)$.
We are asked to compute $\Pr(B|(A\cap \overline{B})\cup(\overline{A}\cap B))$
Can you do it now?