Slot machines are now video games, with winning determined by electronic random

Question

Slot machines are now video games, with winning determined by electronic random number generators. In the old days, slot machines were like this: you pull the lever to spin three wheels; each wheel has 20 symbols, all equally likely to show when the wheel stops spinning: the three wheels are independent of each other. Suppose that the middle wheel has 8 bells among its 20 symbols, and the left and right wheels have 1 bell each. (a) You win the jackpot if all three wheels show bells. What is the probability of winning the jackpot? (Round your answer to four decimal places.) (b) What is the probability that the whees stop with exactly 2 bells showing? (Round your answer to four decimal places.)

Explanation / Answer

a) We have to select 1 bell out of 8 bells, and 1 from each other machine

P = 8/20 * 1/20 * 1/20 = 0.001

b) P = 1/20 * 8/20 * 19/20 * 2 = 304/8000

P = (1/20)^2 * 12/20 = 12/8000

P = 304/8000 + 12/8000 = 0.0395

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