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Q. 104

Expert-verified
Found in: Page 227

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

# 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 $2014$?

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

See the step by step solution

## Step 1 : 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.

## Step 2 : Calculation

The total as:

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

Let R $\cup$U be the probability.

$P\left(R\cup U\right)=P\left(\text{republican}\right)+P\left(\begin{array}{l}up\text{for reelection}\\ \text{in}2014\end{array}\right)-P\left(R\cap U\right)\phantom{\rule{0ex}{0ex}}=\frac{37}{67}+\frac{33}{67}-\frac{13}{67}\phantom{\rule{0ex}{0ex}}=\frac{70}{67}-\frac{13}{67}\phantom{\rule{0ex}{0ex}}=\frac{57}{67}\phantom{\rule{0ex}{0ex}}=0.85$