Question

Slot machines are now video games, with outcomes determined by 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 6 cherries among its 20 symbols, and the left and right wheels have one cherry each.

There are three ways that the three wheels can show two cherries and one symbol other than a cherry. Find the probability of each of these ways. (Use 4 decimal places.)

a. other symbol on right wheel:

b. other symbol on left wheel:

c. the symbol on left wheel:

What is the probability that the wheels stop with exactly two cherries showing among them? (Use 3 decimal places.)

Answer 1

solution:

P( wheel 1 show cherry) =1/20

P( wheel 2 show cherry) =6/20

P( wheel 3show cherry) =1/20

b)other symbol on right wheel P= (1/20)*(6/20)*(19/20) = 0.0143

other symbol on left wheel P =(19/20)*(6/20)*(1/20) = 0.0143

other symbol on middle wheel P=(1/20)*(14/20)*(1/20) = 0.0018

c)p(exactly 2 cherries)=0.0143+0.0143+0.0018

= 0.0304