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\% 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.

Question
Upper level algebra
asked 2021-02-22
Conditional probability if \(\displaystyle{40}\%\) of the population have completed college, and \(\displaystyle{85}\%\) 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.

Answers (1)

2021-02-23
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 \(\displaystyle{34}\%\).
0

Relevant Questions

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The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
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Previous studies show that \( \sigma_1 = 19 \).
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The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
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