Question

Use the two-way frequency table to calculate the probability that the person is a democrat, given theact that the person supports the issue, P(democrat | supports the issue).P(democrat | supports the issue) =(Type an integer or decimal rounded to the nearest hundredth as needed.)

Answer 1

In order to calculate the probability of P(democrat | supports the issue), we can use the following formula for conditional probability:

$\begin{gathered} P(A|B)=\frac{P(A\cap B)}{P(B)} \\ P(democrat|supportstheissue)=\frac{P(democrat\cap supportstheissue)}{P(supportstheissue)} \end{gathered}$

In the right side of the equation, instead of using the probability, we can use the value in the frequency table.

So we have:

$P(democrat|supportstheissue)=\frac{24}{58}=\frac{12}{29}=0.41$