In a casino game, a gambler selects four different numbers from the first twelve positive integers. The casino then randomly draws nine numbers without replacement from the first twelve positive integers. The gambler wins the jackpot if the casino draws all four of the gambler’s selected numbers.

Calculate the probability that the gambler wins the jackpot.

• 0.002
• 0.255
• 0.296
• 0.573
• 0.625

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

This question is equivalent to “What is the probability that 9 different chips randomly drawn from a box containing 4 red chips and 8 blues chips will contain the 4 red chips?” The hypergeometric probability is

[[math]] \frac{\binom{4}{4}\binom{8}{5}}{\binom{12}{9}} \frac{1(56)}{220} = 0.2545. [[/math]]

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.