In the Florida lottery game, you select six numbers from a pool of numbers from 1 to 53 (see flalottery.com). Each wager costs $1. You win the jackpot if you match all six numbers that you have selected (Questions f to i are optional. Questions f to i will not be graded). Find the probability of a) Wining the jackpot. b) Matching five numbers. c) Matching four numbers. d) Matching three numbers. e) Matching two numbers.

Emmanuel Pace 2022-07-19 Answered
In the Florida lottery game, you select six numbers from a pool of numbers from 1 to 53 (see flalottery.com). Each wager costs $1. You win the jackpot if you match all six numbers that you have selected (Questions f to i are optional. Questions f to i will not be graded). Find the probability of a) Wining the jackpot. b) Matching five numbers. c) Matching four numbers. d) Matching three numbers. e) Matching two numbers.
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Answers (1)

Sheldon Castillo
Answered 2022-07-20 Author has 10 answers
a)
P( Wining the jackpot) =P(match 6 out of 6 winning numbers) = C ( 6 , 6 ) C ( 53 , 6 ) = 1 22957480
b)
P( Matching five from 6 numbers and 1 from 47 remaining) = C ( 6 , 5 ) C ( 47 , 1 ) C ( 53 , 6 ) = 6 47 22957480 = 2 162819
c)
P(Matching four numbers)
= C ( 6 , 4 ) C ( 47 , 2 ) C ( 53 , 6 ) = 15 1081 22957480 = 3243 4591496
d)
P(Matching three numbers)= C ( 6 , 3 ) C ( 47 , 3 ) C ( 53 , 6 ) = 20 16215 22957480 = 16215 1147874
e)
P(Matching two numbers)= C ( 6 , 2 ) C ( 47 , 4 ) C ( 53 , 6 ) = 15 178365 22957480 = 535095 4591496

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