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 12 bells among its 20 symbols, and the left and right wheels have 1 bell each. 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.) _____ What is the probability that the wheels stop with exactly 2 bells showing? (Round your answer to four decimal places.) _____

Explanation / Answer

a) You win the jackpot if all 3 wheels show bells. What is th probability of winning the jackpot?

   Answer:      Since eachwheel is independent of the other ,

    P[ winning the jackpot ] = 1/20*12/20*1/20= 0.0015

What is the probability that the wheel stopwith exactly 2 bells showing among them?

P[ exactly 2 bells ] = P[ 1st way with two bells ] + P[ 2ndway with two bells ] + P[ 3rd way with two bells ]

=P[ 1st and 2ndwheels shows a bell and the 3rd does not ]+P[ 1st and 3rdwheels shows a bell and the 2nd does not ]+P[ 2nd and 3rdwheels shows a bell and the 1st does not ]

=1/20*12/20*19/20+1/20*12/20*1/20+19/20*12/20*1/20

                               = 0.0285 + 0.00237 + 0.0285 = 0.0594

Hope this will help you. Thanks :-)

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