## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 11 - Counting Methods and Probability Theory - 11.7 Events Involving And; Conditional Probability - Exercise Set 11.7: 19

#### Answer

$\frac{1}{4}$

#### Work Step by Step

If A and B are independent events, then P(E) = P(A)*P(B) You draw a card from a standard deck of playing cards. Then, after the card that you drew is replaced, you draw another card. Find the probability of some event, E, happening. Let A be the first event, B be the second event, and so on. E: a red card the first and the second time A: {26} a red card B: {26} a red card P(A) = $\frac{26}{52}$ P(B) = $\frac{26}{52}$ Both events A and B are independent: P(E) = $\frac{26}{52}$ .$\frac{26}{52}$ = $\frac{1}{4}$

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