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Q29E

Expert-verifiedFound in: Page 451

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?**

**Answer **

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 $P\left(E\right)=5.37\times {10}^{-12}$.

The positive integers not exceeding 100.

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

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

** **

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:

$P\left(E\right)=\frac{{}^{8}{C}_{8}}{{}^{100}{C}_{8}}\phantom{\rule{0ex}{0ex}}P\left(E\right)=\frac{1}{186087894300}\phantom{\rule{0ex}{0ex}}P\left(E\right)=5.37\times {10}^{-12}\phantom{\rule{0ex}{0ex}}$

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