## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.7 - Probability - Exercise Set - Page 1118: 20

#### Answer

The required probability is, $\frac{3}{13}$

#### Work Step by Step

Note that with 52 cards in the deck, the total number of possible ways in which a single card is dealt is 52. We know that the total number of possible outcomes in the sample space is 52. That is, $n\left( S \right)=52$ Assume $E$ to be the event of being dealt a card greater than 3 and less than 7; therefore, $E=4\text{ or 5 or 6}$ and each of these number can occurs in 12 different ways; therefore, $n\left( E \right)=12$ Thus, the probability of being dealt a card greater than 3 and less than 7 is: \begin{align} & P\left( E \right)=\frac{n\left( E \right)}{n\left( S \right)} \\ & =\frac{12}{52} \\ & =\frac{3}{13} \end{align}

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