Explanation Given: An article in which probability is given and two groups of 56 and 46 numbers and we have to pick 5 numbers from first group and 1 from the second group to get the correct matching number. Formula used: We use the combination formula as: C r n = n ! r ! ( n − r ) ! And the probability of an event E is given using the formula, P ( E ) = n ( E ) n ( S ) = Total favorable outcomes Total outcomes Calculation: 5 numbers out of total 56 numbers will be selected in total C 5 56 as it is a combination problem here. And last number will be taken from a group of 46 numbers, that means total number of ways of selecting winning match, consisting 6 numbers will be C 5 56 × 46 . And as there is a single matching number (winning ticket) we need, total favorable outcomes will be 1 here. Here n = 56 , r = 5 So, n ( S ) = C 5 56 × 46 = 56 ! 5 ! ( 56 − 5 ) !...

Pearson eText for Using & Understanding Mathematics: A Quantitative Reasoning Approach -- Instant Access (Pearson+)

7th Edition

ISBN: 9780137553334

Author: Jeffrey Bennett, William Briggs

Publisher: PEARSON+

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Chapter 7.E, Problem 59E

To determine

Article about a lottery in which choosing a number involves combination:

“The lottery game “Megamillions” is played in over 40 states and requires $1 per ticket to play. To win the jackpot, one must correctly pick five unique numbers from balls numbered 1 through 56 (Order does not matter) and correctly pick the megaball number which is picked from the balls numbered 1 through 46. Thus probability of winning the jackpot remains almost less than ten millionth.”

To determine:

Probability of getting a matching number consisting of 6 numbers in which first 5 numbers we have to select out of 56 numbers and last number will be taken from another group of 46 numbers.

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Chapter 7.E, Problem 58E

Chapter 7.E, Problem 60E

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Chapter 7 Solutions

Pearson eText for Using & Understanding Mathematics: A Quantitative Reasoning Approach -- Instant Access (Pearson+)

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