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

Question

Powerball is a lottery game where 5 white balls are drawn from a drum with 59 balls (numbered 1-59) and one red ball 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 cach 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 correctly Pick 3 white balls + 1 red ball correctly Pick 3 white balls correctly Pick 2 white balls + 1 red ball correctly Pick 1 white ball + 1 red ball correctly Pick 1 red ball correctly Amount $10,000,000 $1,000,000 $10,000 $100 $100 $7 $7 $4 $4

Explanation / Answer

Solving First 4 parts, Please repost the rest individually

a) All 6 correctly =5 numbers to be selected from 59 out of which only one combnation is correct* 1 number to be selected of 35 1/ 59C5 * 1/35

b) All 5 correct = 1/59C5 * 34/35

c) 4 correct and red correct - 1/59C5 * 5*54 * 1/35

d) 4 correct = 1/59C5 * 5*54 * 34/35

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