Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.7 - Probability - Exercise Set - Page 1119: 29

Answer

$\frac{2125}{29285256}$

Work Step by Step

Step 1. Choose 5 numbers from $1\ to\ 56$. We have $_{56}C_5$ combinations. Step 2. Choose 1 number from $1\ to\ 46$. We have 46 choices. Step 3. The total sample space is $46\times_{56}C_5$ Step 4. To win the prize, we need to match 3 numbers out of 5 or $_{5}C_3$, leaving 2 balls in $51$ (non-winning balls) or $_{51}C_2$. Thus the total ways for this part is $_{51}C_2\times_{5}C_3=12750$ Step 5. There is only one way to select the gold ball. Thus the total ways of winning is $12750$ Step 6. The probability of winning this prize is $p=\frac{12750}{46\times_{56}C_5}=\frac{12750}{46(3819816)}=\frac{2125}{29285256}$
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