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.

What is the probability that a randomly selected is a Republican or is up for reelection in November $2014$?

Short answer

The probability of the randomly selected Republican or reelection in November $2014$is $P(R\cup U)=0.85\text{.}$

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 Republican winning reelection in November $2014$is computed as follows:

Let R $\cup$U be the probability.

$$\begin{gathered} P(R\cup U)=P\left(\text{republican}\right)+P\left(\begin{array}{l}up\text{for reelection}\\ \text{in}2014\end{array}\right)-P(R\cap U) \\ =\frac{37}{67}+\frac{33}{67}-\frac{13}{67} \\ =\frac{70}{67}-\frac{13}{67} \\ =\frac{57}{67} \\ =0.85 \end{gathered}$$