## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.7 - Probability - Exercise Set - Page 1119: 43

#### Answer

The probability that a 7 or a red card is dealt from a pack of 52 cards is $\frac{7}{13}$.

#### Work Step by Step

We know that the total number of 7 cards in a deck is 4. \begin{align} & P\left( \text{7} \right)=\frac{\text{number of 7 cards}}{\text{total number of cards in the deck}} \\ & =\frac{4}{52} \\ & =\frac{1}{13} \end{align} And the total number of red cards in a deck is 26. \begin{align} & P\left( \text{red} \right)=\frac{\text{number of red cards}}{\text{total number of cards in the deck}} \\ & =\frac{26}{52} \\ & =\frac{1}{2} \end{align} And the total number of red 7 cards in a deck is 2. \begin{align} & P\left( \text{7 or red} \right)=\frac{\text{number of red 7 cards}}{\text{total number of cards in the deck}} \\ & =\frac{2}{52} \\ & =\frac{1}{26} \end{align} Therefore, the probability that a 7 or a red card is dealt is given below, \begin{align} & P\left( \text{a 7 or a red card} \right)=P\left( 7 \right)+P\left( \text{red} \right)-P\left( 7\text{ or red} \right) \\ & =\frac{1}{13}+\frac{1}{2}-\frac{1}{26} \\ & =\frac{7}{13} \end{align} Thus, the probability that a 7 or a red card is dealt is $\frac{7}{13}$.

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