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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.

Short Answer

Expert verified

The probability of selecting the correct five numbers is 1962598.

Step by step solution

01

Given Information

Five number cards are selected from 1 to 43.

The number of the top prize card combination is 1.

02

Define the probability of an event and the combination rule

The formula for the probability of an event A is:

PA=NumberoffavorableoutcomesTotalnumberofoutcomes

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:

Crn=n!n-r!脳r!

03

Compute the total outcomes

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

43C5=43!43-5!5!=962598

04

Compute the probability of correct five numbers

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

The probability of winning the top prize is:

PE=1962598

Thus, the probability of winning the top prize is 1962598.

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Negative Test Result

(Test shows no drug use)

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45 (True Positive)

5 (False Negative)

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