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 25 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 16 bells among its 25 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.)

Answer 1

Answer:

Given that:

Suppose that the middle wheel has 16 bells among its 25 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?

Find the probability of winning the jackpot

P(Jackpot) = 1/25 *16/25*1/25

= (0.04)(0.64)(0.04)

= 0.0010

Thus, the probability of winning the jackpot is 0.0010

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

Find the probability that the wheels stop with exactly 2 bells showing

= 1/25*16/25*24/25*2

= (0.04)(0.64)(1.92)

= 0.0492

=

= (0.0016)(0.36)

= 0.0006

The required probability is

p(Wheels stop with exactly 2 bells) = 0.0492+0.0006

= 0.0498

Thus, the probability that the wheels stop with exactly 2 bells showing is 0.0498