A standard slot machine has three wheels that spin independe

A standard slot machine has three wheels that spin independently. Each wheel has 10 equally likely symbols: 4 bars, 3 lemons, 2 cherries, and 1 bell. If you play once, what is the probability you will get:

(a) 3 lemons?

(b) No fruit symbols?

(c) 3 bells (the jackpot)?

(d) No bells?

(e) At least one bar (an automatic loser)?

Solution

A)

Note that P(lemon) = 3/10 = 0.3.

Thus,

P(all 3 lemons) = 0.3^3 = 0.027 [ANSWER]

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B)

Note that

P(not fruit) = 5/10 = 0.5

Thus,

P(all 3 are not fruits) = 0.5^3 = 0.125 [ANSWER]

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c)

It is the same as part B,

P(all 3 bells) = 0.1^3 = 0.001 [ANSWER]

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D)

P(not bell) = 1 - P(bell) = 1 - 0.1 = 0.9.

Thusm

P(all 3 are not bells) = 0.9^3 = 0.729 [ANSWER]

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e)

Here, P(not bar) = 1 - 4/10 = 0.6.

P(at least 1 bar) = 1 - P(no bar)

= 1 - 0.6^3

= 0.784 [ANSWER]