Slot machines have three drums with the same number of positions on each drum. Each position contains a symbol. When you pull the lever on the machine, the drums spin. Assume that each drum is equally likely to stop in any position, and that the positions in which the three drums stop are independent of each other and independent from spin to spin. Suppose a particular slot machine has 12 positions on each drum, and that each position contains one of two symbols: an eggplant or a grapefruit. You win the jackpot if all three drums stop with eggplants showing. The first drum has 7 eggplants and 5 grapefruits, the second has 8 eggplants and 4 grapefruits, and the third drum has 1 eggplant and 11 grapefruits. In each pull of the lever, the probability of winning the jackpot is (Q1)
The number of times I win the jackpot in 20 attempts has (Q2)
The probability of winning the jackpot at least once in 20 attempts is (Q3)
The number of attempts it takes to win the first jackpot has (Q4)
The probability that it takes exactly 20 attempts to win the jackpot the first time is (Q5)
The number of attempts it takes to win the jackpot for the fourth time has (Q6)
The chance that I win the jackpot for the fourth time on my twentieth attempt is (Q7)