2. Powerball is a lottery game where 5 white balls are drawn from a drum with 59

Question

2. Powerball is a lottery game where 5 white balls are drawn from a drum with 59 balls (numbered 1-59) and one red ba is drawn from a drum with 35 balls (numbered 1-35) Players guess the value of all balls and win a prize if they guess correctly. Players win the following amounts based on the indicated matching sequence. Calculate the probability of winning each of the prizes listed below. (9 pts) Matching sequence Pick all 6 correctly Pick 5 white balls correctly Pick 4 white balls+1 red ball correctly Pick 4 white balls cormrectly Pick 3 white balls +1 red ball correctly S100 Pick 3 white balls correctly Pick 2 white balls+1 red ball correctly Pick 1 white ball red ball correctly Pick 1 red ball correctly Amount S10,000,000 S1,000,000 $10,000 S100 S7 S7 $4 S4

Explanation / Answer

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Here' all answers with exact formulae :

a. P(pick all 6 correctly) = 5C5/59C5 * 1C1/15C1 = 5.71*10^-9

b. P(pick 5 white balls correctly) = 5C5/59C5 = 2*10^-7

c. P(pick 4 white + 1 red correctly) = 5C4/59C4 * 1C1/35C1 = 3.14*10^-7

d. P(pick 4 white correctly) = 5C4/59C4 = 1.09*10^-5

e. P(pick 3 white balls + 1 red ball) = (5C3/59C3) * (1C1/35C1) = 8.8*10^-7

f. P(3 white balls) = (5C3/59C3) = 3*10^-4

g. P(2 white balls + 1 red) = (5C2/59C2)*(1/35C1) = 1.67*10^-5

h. P(1 white + 1 red) = 5C1/59C1 * (1C1/15C1) = (5/59) * (1/35) = 2.42*10^-3

i. P( 1 red correeclty) = 1/35C1 =.029

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