Question

A slot machine has 5 reels each with 9 symbols one of which is a Jackpot.

How many different outcomes will occur after one spin?

What is the possibility of atleast one jackpot?

What is the possibility of no jackpots?

What is the possibility of 3 jackpots?

Answer 1

a) The number of different outcomes that can occur in a spin is computed here as: (Using multiplication rule)
= Number of different outcomes in the first reel* Number of second outcome in the second reel and so on..

= 9*9*....... 5 times

= 95

= 59049

Therefore 59049 different outcomes are possible here.

b) The probability of at least one jackpot is computed here as:
= Total number of possible outcomes - Total number of outcomes with no jackpots

= 59049 - 8*8*... 5 times

= 59049 - 85 = 26281

Therefore there are 26281 outcomes with at least one jackpot here. Therefore the probability of at least one jackpot is computed here as:
= Total outcomes with at least one jackpot / Total outputs

= 26281 / 59049

= 0.4451

Therefore 0.4451 is the required probability here.

c) For no jackpots, the probability is computed here as:
= 1 - Probability of at least one jackpot

= 1 - 0.4451

= 0.5549

Therefore 0.5549 is the required probability here.

d) The probability of 3 jackpots is computed here as:
= Number of ways to select 3 reel out of the 5 reels which will have the jackpots * Number of ways to select an outcome for each of the remaining 2 reels / Total outcomes possible

Therefore 0.0108 is the required probability here.