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

(i) Matching exactly three of the five balls and the powerball or 

(ii) Matching exactly four of the five balls and not the powerball. 

Find the probability of winning $100.

Data from Example 3.16.

In the Powerball lottery, the player picks five numbers between 1 and 59 and then a single €œpowerball€ 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(⁵⁹C₅) possible plays. Of these, one is the jackpot winner. The desired probability is

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 other five numbers. The number of ways to make such a match is (⁵C₄)(⁵⁴C₁), selecting the powerball winner, four of the five nonpowerball winners, and one loser. The desired probability is

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

Transcribed Image Text:

'59 = 5.707 x 10-, P(Jackpot) = 1 / 35 5. P($10,000) : O)/=( 59 35 = 1.54089 x 10-6,