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Expert-verified Found in: Page 451 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # Question:In a super lottery, a player wins a fortune if they choose the eight numbers selected by a computer from the positive integers not exceeding 100. What is the probability that a player wins this super lottery?

The probability that a person wins the grand prize by picking 7 numbers that are among the 11 numbers selected at random by a computer, provided a player selects 7 numbers out of the first 80 positive integers is $P\left(E\right)=5.37×{10}^{-12}$.

See the step by step solution

## Step 1:  Given

The positive integers not exceeding 100.

## Step 2: The Concept of Probability

If ${\mathbit{S}}$ represents the sample space and ${\mathbit{E}}$ represents the event. Then the probability of occurrence of favourable event is given by the formula as below:

${\mathbit{P}}{\mathbf{\left(}}{\mathbit{E}}{\mathbf{\right)}}{\mathbf{=}}\frac{\mathbf{n}\mathbf{\left(}\mathbf{E}\mathbf{\right)}}{\mathbf{n}\mathbf{\left(}\mathbf{S}\mathbf{\right)}}$

## Step 3: Determine the probability

As per the problem we have been asked to find the probability that a person wins the grand prize by picking 8 numbers selected by a computer from the positive integers not exceeding 100.

If $S$ represents the sample space and $E$ represents the event. Then the probability of occurrence of favourable event is given by the formula as below:

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$.

So, the number of possible ways of select 8 numbers out of the first 100 positive integers is $n\left(s\right){=}^{100}{C}_{8}$.

Total number of ways that the 8 numbers selected by a player to be in 8 numbers selected by computer at random is $n\left(E\right){=}^{8}{C}_{8}$.

There will be only one set of positive integers for which lottery can be drawn.

The probability that a person wins the grand prize by picking 8 numbers selected by a computer from the positive integers not exceeding 100 is as follows:

$P\left(E\right)=\frac{{}^{8}{C}_{8}}{{}^{100}{C}_{8}}\phantom{\rule{0ex}{0ex}}P\left(E\right)=\frac{1}{186087894300}\phantom{\rule{0ex}{0ex}}P\left(E\right)=5.37×{10}^{-12}\phantom{\rule{0ex}{0ex}}$ ### Want to see more solutions like these? 