Chapter 4: Q16 (page 180)

Pennsylvania Cash 5 In the Pennsylvania Cash 5 lottery, winning the top prize requires that you select the correct five different numbers between 1 and 43 (in any order). What is the probability of winning the top prize? Express the answer as a fraction.

Expert verified

The probability of selecting the correct five numbers is $\frac{1}{962598}$ .

Step by step solution

Five number cards are selected from 1 to 43.

The number of the top prize card combination is 1.

The formula for the probability of an event A is:

$P (A) = \frac{Number of favorable outcomes}{Total number of outcomes}$

Often the total number of outcomes and favorable outcomes are computed using the combination rule.

The formula of the combination rule for selecting ritems from n is:

${}^{n}{C_{r}} = \frac{n!}{(n - r)! \times r!}$

The number of ways to select five cards from 43 is:

$^{43} C_{5} = \frac{43!}{(43 - 5)! 5!} = 962598$

Define event E as the probability of winning the top prize.

The probability of winning the top prize is:

$P (E) = \frac{1}{962598}$

Thus, the probability of winning the top prize is $\frac{1}{962598}$ .

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	Purchased Gum	Kept the Money
Students Given Four Quarters	27	46
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