# 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.

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