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Chapter 7: Problem 13

Five hundred raffle tickets were sold. What is the probability that a person holding one ticket will win the first prize? What is the probability that he or she will not win the first prize?

Short Answer

Expert verified
The probability of a person holding one ticket winning the first prize is \( P(win) = \frac{1}{500} \). The probability of a person holding one ticket not winning the first prize is \( P(not \thinspace win) = \frac{499}{500} \).

Step by step solution

01

Identify the total number of outcomes

In this raffle, 500 tickets were sold. This means that there are 500 possible outcomes, as each ticket has an equal chance of winning.
02

Calculate the probability of winning the first prize

To find the probability of winning the first prize, we need to find the ratio of favorable outcomes to the total number of outcomes. In this case, the favorable outcome is holding the winning ticket, which is 1 (as there is only one first prize). So, the probability of winning the first prize is: \( P(win) = \frac{favorable \thinspace outcomes}{total \thinspace outcomes} = \frac{1}{500} \)
03

Calculate the probability of not winning the first prize

To find the probability of not winning the first prize, we need to find the number of unfavorable outcomes (not winning) and divide it by the total number of outcomes. The number of unfavorable outcomes is the total number of tickets minus the winning ticket, which is \(500 - 1 = 499\). So, the probability of not winning the first prize is: \( P(not \thinspace win) = \frac{unfavorable \thinspace outcomes}{total \thinspace outcomes} = \frac{499}{500} \)
04

Write the final answer

The probability of a person holding one ticket winning the first prize is: \( P(win) = \frac{1}{500} \) The probability of a person holding one ticket not winning the first prize is: \( P(not \thinspace win) = \frac{499}{500} \)

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