Stuck on part b, don\'t know how to do it.
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?
b) What is the probability that the wheels stop with exactly 2 bells showing?
Stuck on part b, don\'t know how to do it.
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?
b) What is the probability that the wheels stop with exactly 2 bells showing?
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?
b) What is the probability that the wheels stop with exactly 2 bells showing?
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?
b) What is the probability that the wheels stop with exactly 2 bells showing?
There are 3 wheels say wheel 1, 2 and 3.
EAch wheel has 20 symbols.
All three wheels are independent and each symbol is equally likely
Hence prob for a wheel to show one symbol = 1/20 = 0.05
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The middle wheel turning to a bell has prob 8/20 = 0.4
The other two wheel has prob for a bell = 1/20 = 0.05
a) Prob for winning jackpot = prob all three wheels show bell
=P(ABC) = P(A)P(B)P(C) (as the wheels are independent)
= 0.05(0.4)(0.05)
= 0.01
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b) Prob that the wheels stop with exactly 2 bells showing
= P(ABC\'U AB\'CUA\'BC) (where A is the first wheel showing bell , A\' first wheel not showing bell , etc)
= P(ABC\')+P(AB\'C)+P(A\'BC)
= P(A)P(B)P(C\')+P(A)P(B\')P(C)+P(A\')P(B)P(C)
= 0.05(0.4)(0.95)+0.05(0.6)(0.05)+0.05(0.4)(0.95)
= 0.038+0.0015
= 0.0395
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