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 10 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 5 eggplants and 5 grapefruits, the second has 2 eggplants and 8 grapefruits, and the third drum has 8 eggplants and 2 grapefruits.
The chance that I win the jackpot for the third time on my fifteenth attempt is