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Q29E

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Discrete Mathematics and its Applications
Found in: Page 451
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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Short Answer

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(E)=5.37×10-12.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1:  Given  

The positive integers not exceeding 100.

Step 2: The Concept of Probability

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(E)=n(E)n(S)

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(E)=n(E)n(S).

So, the number of possible ways of select 8 numbers out of the first 100 positive integers is n(s)=100C8.

Total number of ways that the 8 numbers selected by a player to be in 8 numbers selected by computer at random is n(E)=8C8.

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(E)=C88C8100P(E)=1186087894300P(E)=5.37×10-12

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