Question

Use the information in the Table $3.19$to answer the next eight exercises. The table shows the political party affiliation of each of $67$members of the US Senate In June $2012$. and when they are up freelection.

Suppose that a member of the US Senate is randomly selected. what is the probability that the senator Is up for reelection in November $2014$, knowing that this senator is a Republican?

Short answer

The probability of the reelection in November $2014$ , where the senator is a Republican is$P\left(R\right)=0.35$.

Step-by-step solution

Given

The table shows the political party affiliation of each of $67$members of the US Senate In June $2012$. and when they are up freelection.

Calculation  

The total as:

The chance of reelection in November 2014 for a Republican senator is computed as :

Let the probability be R.

$$\begin{gathered} P\left(R\right)=\frac{n\left(R\right)}{n\left(S\right)} \\ n\left(R\right)=13;n\left(S\right)=37 \\ P\left(R\right)=\frac{13}{37} \\ =0.35 \end{gathered}$$