Question

A fair spinner has 9 equal sections: 3 red, 2 blue and 4 green.

It is spun twice.
What is the probability of not getting two consecutive reds?

Answer 1

The probability of not getting two consecutive reds is therefore 36/81, or approximately 0.44.

Explanation:

There are a total of 9 * 9 = 81 possible outcomes when the spinner is spun twice. The probability of not getting two consecutive reds is equal to the number of outcomes that do not result in two consecutive reds divided by the total number of outcomes.

There are 3 * 6 = 18 outcomes that result in two reds, but they are not consecutive. These outcomes are: (red, blue), (red, green), (blue, red), (green, red), (blue, green), (green, blue).

There are 3 * 2 = 6 outcomes that result in one red and one blue. These outcomes are: (red, blue), (blue, red), (blue, green), (green, blue), (green, red), (red, green).

There are 3 * 4 = 12 outcomes that result in one red and one green. These outcomes are: (red, green), (green, red), (green, blue), (blue, green), (blue, red), (red, blue).

So, there are a total of 18 + 6 + 12 = 36 outcomes that do not result in two consecutive reds.

The probability of not getting two consecutive reds is therefore 36/81, or approximately 0.44.