Conditional probability if 40\% of the population have completed college, and 85\% of college graduates are registered to vote, what percent of the population areboth college graduates andregistered voters? To find: The percent of people who is both college graduates and registered voters.

Approach:
Conditional probability is the probability of an event occurring based on the occurrence of a previous event.
In other words, ${\displaystyle P\left(B\mid A\right)}$ is a conditional probability that the event B will occur given that another event A has already occurred. In this case, A and B are dependent events.
${\displaystyle P\left(B\mid A\right)}$ is ead as the conditional probability of B given A.
Multiplication property of probabilities: For events A and B, ${\displaystyle P(A\cap B)=P\left(A\right)\cdot P\left(B\mid A\right)=P\left(B\right)\cdot P\left(A\mid B\right)}$.
Given:
${\displaystyle 40\mathrm{\%}}$ of the population is college graduates and ${\displaystyle 85\mathrm{\%}}$ of college graduates are registered voters.
Calculation:
Let P(A) be the probability that a person have completed college and let ${\displaystyle P\left(B\mid A\right)}$ is the probability that a college graduates are registered to vote.
According to question, ${\displaystyle P\left(A\right)=0.4}$ and ${\displaystyle P\left(B\mid A\right)=0.85}$.
The probability that a person is both college graduates and registered voters is ${\displaystyle P(A\cap B)}$.
The probability of occurrence of both A and Bcan be found by using multiplication property of probabilities.
Substitute ${\displaystyle P\left(A\right)=0.4}$ and ${\displaystyle P\left(B\mid A\right)=0.85}$ in ${\displaystyle P(A\cap B)=P\left(A\right)-P\left(B\mid A\right)}$.
${\displaystyle P(A\cap B)=\left(0.4\right)\cdot \left(0.85\right)=0.34}$
Final statement:
Therefore, the population is both college graduates and registered voters is ${\displaystyle 34\mathrm{\%}}$.