See Example 3.16 for a description of the Powerball lottery. A $100 prize is got

Question

See Example 3.16 for a description of the Powerball lottery. A $100 prize is gotten by either (i) matching exactly four of the five balls and the power or (ii) matching exactly four of the five balls and not the Powerball. Find the probability of winning $100.

(Example 3.16 Lottery. In the Powerball lottery, the player picks five numbers between 1 and 59 and then a single “Powerball” number between 1 and 35. To win the jackpot, you need to match all six numbers. What is the probability of winning the jackpot? There are 35(59 over 5) possible plays. Of these, one is the jackpot winner. The desired probability is

P(Jackpot) = 1 / 35 (59 over 5) = 5.707 X 10^-9,

Almost 1 out of 200 million.

You can win $10,000 in the Powerball lottery if you match the Powerball and exactly four of the five numbers. The number of ways to make such a match is (5 over 4)(54 over 1), selecting the Powerball winner, four of the five nonpowerball winners, and one loser. The desired probability is

P(10,000) = (5 over 4)(54 over 1)/35(59 over 5) = 1.54089 x 10^-6,

about the same as the probability of being dealt a royal straight flush in poker.)

Explanation / Answer

To win the lottery, exactly 4 of 5 balls must be matched and the Powerball is matched or not isn't relevant

The probability of matching a ball = 54C1 / 59C5 = 0.00001078622 (As we can choose 5 numbers from 59 in 59C5 ways. 4 of them must be same and one is different. So different number can be any of the remaining 59-5 = 54)

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