For the Powerball, 5 white balls are drawn out of a drum with 59 balls and one r

Question

For the Powerball, 5 white balls are drawn out of a drum with 59 balls and one red ball being drawn out of a drum with 35 red balls. You already know that the probability of winning the jackpot with one ticket is 5.707 x 10-9. Find:

a. The probability of winning the second prize (won by matching five white balls in any order without matching the red ball).

b. The probability of winning the third prize (won by matching only the red ball).

c. The probability of winning any of the first three prizes.

Explanation / Answer

a) P(Winning second prize) = P(White balls match but red doesn't match) = 5! / 59C5 * 34/35 = 2.328 x 10^(-5)

b) P(Winning third price) = P(Only red match) = (1 - 5!/ 59C5) * 1/35 = 0.02857

c) P(Winning any of the first three prices) = 5.707 * 10^(-9) + 2.328 * 10^(-5) + 0.02857 = 0.028593

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