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, \(\displaystyle{P}{\left({A}\cap{B}\right)}={P}{\left({A}\right)}\cdot{P}{\left({B}{\mid}{A}\right)}={P}{\left({B}\right)}\cdot{P}{\left({A}{\mid}{B}\right)}\).

Given:

\(\displaystyle{40}\%\) of the population is college graduates and \(\displaystyle{85}\%\) 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 \(\displaystyle{P}{\left({A}\cap{B}\right)}\).

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 \(\displaystyle{P}{\left({A}\cap{B}\right)}={P}{\left({A}\right)}-{P}{\left({B}{\mid}{A}\right)}\).

\(\displaystyle{P}{\left({A}\cap{B}\right)}={\left({0.4}\right)}\cdot{\left({0.85}\right)}={0.34}\)

Final statement:

Therefore, the population is both college graduates and registered voters is \(\displaystyle{34}\%\).

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, \(\displaystyle{P}{\left({A}\cap{B}\right)}={P}{\left({A}\right)}\cdot{P}{\left({B}{\mid}{A}\right)}={P}{\left({B}\right)}\cdot{P}{\left({A}{\mid}{B}\right)}\).

Given:

\(\displaystyle{40}\%\) of the population is college graduates and \(\displaystyle{85}\%\) 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 \(\displaystyle{P}{\left({A}\cap{B}\right)}\).

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 \(\displaystyle{P}{\left({A}\cap{B}\right)}={P}{\left({A}\right)}-{P}{\left({B}{\mid}{A}\right)}\).

\(\displaystyle{P}{\left({A}\cap{B}\right)}={\left({0.4}\right)}\cdot{\left({0.85}\right)}={0.34}\)

Final statement:

Therefore, the population is both college graduates and registered voters is \(\displaystyle{34}\%\).