Question

A slot machine at a casino consists of three reels which spin when the button

is pushed, so that one image on each reel is shown at the end. If each of the three reels has

five equally likely images on it, and each reel functions independently of the other two, find

the following probabilities.

(a) How many sample points are there? What is the probability of each sample point?

(b) Find the probability that the same image appears on each of the three reels.

(c) Find the probability that at least one of three images is different.

Answer 1

a) Total three reels and each has 5 images so total sample points = 5*5*5 = 125

Probability of each sample point = 1/125

b) P(same image on all three) =

Hence the probability that the same image appears on each of the three reels = 1/25 or 0.04.

Here we took 5 in numerator because total 5 images are possible which can be same in all three reels and 125 in denominator because that's the total number of sample points possible there.

c) P(at least one different) = 1 - P(all same)

Hence, the probability that at least one of three images is different is 24/25 or 0.96.

Please comment if any doubt. Thank you.