Explanation Given information: A player selects six numbers from 1 to 49 in a 6 / 49 lottery game. The player wins if the player selects the winning six numbers. Concept used: The probability P ( E ) of any event E can be calculated as, P ( E ) = n ( E ) n ( S ) ............ (1) Here, n ( E ) is the total number of elements in event E and n ( S ) is the number of element in sample space of an experiment. The probability of event E and F can be expressed as, P ( E ∩ F ) = P ( E ) P ( F ) ............ (2) Here, the event E and F are independent events in a sample space S . Calculation: The sample space is the total possible outcomes in an experiment. Consider n ( S ) as total the number of ways of choosing six numbers in 6 / 49 lottery game such that it denotes the sample space S . The number of ways of choosing six numbers from 1 to 49 in a sample space is, n ( S ) = C ( 49 , 6 ) Consider A as the event that the player wins the lottery first time, n ( A ) as the number of ways of choosing six numbers in event A and P ( A ) as the probability of event A . The number of element in event A can be calculated as, n ( A ) = C ( 6 , 6 ) To obtain the probability P ( A ) , replace A by E in the equation (1) as, P ( A ) = n ( A ) n ( S ) ............ (3) Substitute C ( 6 , 6 ) for n ( A ) and C ( 49 , 6 ) for n ( S ) in the equation (3) to obtain the probability P ( A ) as, P ( A ) = C ( 6 , 6 ) C ( 49 , 6 ) = 6 ! 6 ! ( 6 − 6 ) ! 49 ! 6 ! ( 49 − 6 ) ! = 1 49 ⋅ 48 ⋅ 47 ⋅ 46 ⋅ 45 ⋅ 44 ( 43 ! ) 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 ( 43 ! ) = 1 13983816 Consider B as the event that the player wins the lottery second time, n ( B ) as the number of ways of choosing six numbers in event B and P ( B ) as the probability of event B

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 9.2, Problem 60E

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The probability of winning the lottery two times in a row.

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Chapter 9.2, Problem 59E

Chapter 9.2, Problem 61E

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The probability of winning the lottery two times in a row.

Solution Summary: The author explains how the probability of winning the lottery two times in a row is 5.11times 10-15.

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To find:

The probability of winning the lottery two times in a row.