Question

The probability that a student takes a history class and a sociology class is 0.051. The probability that a student takes a history class is 0.32. What is the probability that a student takes a sociology class given that the student is taking a history class?

0.051

0.159

0.269

0.32

Answer 1

Use Bayes' rule:

\[P(A|B) = \frac{P(A \textrm{ and } B)}{P(B)}\]

Answer 2

So, it's \[\frac{0.051}{0.32} = 0.159\]

Answer 3

thank you! do you mind helping me with another question on probability?

Answer 4

Yeah, sure

Answer 5

A political candidate wanted to understand what issues were important to their voters. They asked 1000 voters, "Which issue is the most important: crime, city planning, or health care?" The results of the survey are shown in the two-way table below:


Crime City Planning Health Care
Male 118 239 458
Female 418 317 449


What is the probability that a person chosen at random from this survey is concerned about crime given that they are male? Round your answer to the nearest tenth.

5.9%

14.5%

22.0%

26.8%

Answer 6

So, you could use Bayes' rule, but it's easier just to disregard the female statistics and only look at the male line. The probability is 118/(118+239+458) = 0.145 = 14.5%.