Question

In a lottery game, the jackpot is won by selecting five different whole numbers from 1 through 41 and getting the same five numbers (in any order) that are later drawn. In the Pick 3 game, you win a straight bet by selecting three digits (with repetition allowed), each one from 0 to 9, and getting the same three digits in the exact order they are later drawn. The Pick 3 game returns $500 for a winning $1 ticket. Complete parts (a) through (c) below.

A. In a lottery game, the jackpot is won by selecting five different whole numbers from 1 through 41 and getting the same five numbers (in any order) that are later drawn. What is the probability of winning a jackpot in this game?

B. In the Pick 3 game, you win a straight bet by selecting three digits (with repetition allowed), each one from 0 to 9, and getting the same three digits in the exact order they are later drawn. What is the probability of winning thisgame?

C. The Pick 3 game returns $500 for a winning $1 ticket. What should be the return if the lottery organization were to run this game for no profit?

Answer 1

A.

select 5 different numbers from 1-41, i.e. 41 numbers

no. of ways = 41C2 = 41! / (2!)*(41-2)! = 820

p(winning) = 1 / no. of ways

= 1 / 820 = 0.0012

p(winning) = 0.0012

B.

0 to 9 : 10 options for each pick

no. of ways = (no. of option for each pick)^(no. of digits to be pocked)

= (10)^3

= 1000

P(winning) = 1/(no. of ways)

= 1 / 1000

= 0.001

p(winning) = 0.001

C.

for no profit :

price of ticket = p(winning) * (return)

$1 = (0.001) * return   {p(winning) = 0.001 calculated in previous part}

return = $1 / (0.001)

= $1000

the return should be $1000 if the lottery organization were to run this game for no profit

(please UPVOTE)