Short Answer

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 $P (R \cup U) = 0.85 .$

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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.

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

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