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.

(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 wheels stop with exactly 2 bells showing? (Round your answer to four decimal places.)

Explanation / Answer

BM = Event of Bell showing on the middle wheel;

P(BM) = Number of bells on the middle wheel / Total number of symbols = 12/20 =3/5

P(Not BM) = 1-3/5 = 2/5

BL = Event of Bell showing on the left wheel

P(BL) =  Number of bells on the left wheel / Total number of symbols = 1/20

P(Not BL) = 1-1/20 = 19/20

BR = Event of Bell showing on the right wheel

P(BR) =  Number of bells on the right wheel / Total number of symbols = 1/20

P(Not BR) = 1-P(BR) = 1-1/20 = 19/20

(a) Probability of winning the jackpot = Probability that all three wheels show bells = P(BM and BL and BR) = P(BM)xP(BL)xP(BR) = (3/5)(1/20)(1/20) = 3/2000 = 0.0015

(b) probability that the wheels stop with exactly 2 bells showing

Event of two wheels stop with exactly 2 bells showing happens when one of the following event happens :

1. Left and Middle wheels stop with bells showing and Right wheel not showing bells : BL and BM and not BR (OR)

2. Right and Middle wheel stop with bells showing and Left wheel not showing bells : BR and BM and not BL (OR)

3. Left and Right wheel stop with bells showing and middle wheel not showing bells : BL and BR and not BM

P(BL and BM and not BR) = 1/20 x 3/5 x 19/20 = 57/2000

P(BR and BM and Not BL) = 1/20 x 3/5 x 19/20 = 57/2000

P(BL and BR and Not BM) = 1/20 x 1/20 x 2/5 = 2/2000

Probability that the wheels stop with exactly 2 bells showing = 57/2000 + 57/2000 + 2/2000=116/2000 = 0.058

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.