Now, let's determine the probability of getting all 3 numbers after four spins of our roulette wheel.

First, we calculate that there are 3⁴ (or 81) results after 4 spins.
Notice that in this case, it is much more difficult to determine and to list these 81 results than it was when we were listing just 27 numbers.

1 1 1 1     1 1 1 2     1 1 1 3     1 1 2 1     1 1 2 2     1 1 2 3     1 1 3 1     1 1 3 2     1 1 3 3     1 2 1 1     1 2 1 2     1 2 1 3     1 2 2 1     1 2 2 2     1 2 2 3     1 2 3 1     1 2 3 2     1 2 3 3     1 3 1 1     1 3 1 2     1 3 1 3     1 3 2 1     1 3 2 2     1 3 2 3     1 3 3 1     1 3 3 2     1 3 3 3     2 1 1 1     2 1 1 2     2 1 1 3     2 1 2 1     2 1 2 2     2 1 2 3     2 1 3 1     2 1 3 2     2 1 3 3     2 2 1 1     2 2 1 2     2 2 1 3     2 2 2 1     2 2 2 2     2 2 2 3     2 2 3 1     2 2 3 2     2 2 3 3     2 3 1 1     2 3 1 2     2 3 1 3     2 3 2 1     2 3 2 2     2 3 2 3     2 3 3 1     2 3 3 2     2 3 3 3     3 1 1 1     3 1 1 2     3 1 1 3     3 1 2 1     3 1 2 2     3 1 2 3     3 1 3 1     3 1 3 2     3 1 3 3     3 2 1 1     3 2 1 2     3 2 1 3     3 2 2 1     3 2 2 2     3 2 2 3     3 2 3 1     3 2 3 2     3 2 3 3     3 3 1 1     3 3 1 2     3 3 1 3     3 3 2 1     3 3 2 2     3 3 2 3     3 3 3 1     3 3 3 2     3 3 3 3   That list of 81 numbers contains all the results of 4 spins of a three-numbered roulette wheel. Next, we must search that list to see how many of those 81 numbers contain "1 2 3 " in any order. It turns out that there are 36 such occurrences:   1 1 2 3     1 1 3 2     1 2 1 3     1 2 2 3     1 2 3 1     1 2 3 2     1 2 3 3     1 3 1 2     1 3 2 1     1 3 2 2     1 3 2 3     1 3 3 2     2 1 1 3     2 1 2 3     2 1 3 1     2 1 3 2     2 1 3 3     2 2 1 3     2 2 3 1     2 3 1 1     2 3 1 2     2 3 1 3     2 3 2 1     2 3 3 1     3 1 1 2     3 1 2 1     3 1 2 2     3 1 2 3     3 1 3 2     3 2 1 1     3 2 1 2     3 2 1 3     3 2 2 1     3 2 3 1     3 3 1 2     3 3 2 1   We see there are 36 ways out of 81 that we can get all 3 numbers after four spins of the wheel. Therefore, the probability of that occurring is: 36 ÷ 81 = .44444444... By now, you are probably thinking that there must be an easier way to do these calculations ... and there is. Click here to go to Page 3 Return To Home Page Copyright © 1999 - 1728 Software Systems