A spinner is separated into 5 equal pieces, as shown below: patrick spins the spinner 9 times. what is the theoretical probability that it stops on the brown sector on the last spin?

To solve this problem, let us first define what probability means in this case. It would be:

Probability = (number of colors to choose from) / (total number of colors)

There are a total of 5 colors on the spinner. The number of colors to choose from spins 1 to 8 would be 5 out of 5, while for the last spin 9 the number of colors to choose from would only be brown so that would be 1 out of 5. The total probability would be the product of the probability of each spins, therefore:

Probability = 1st spin * 2nd spin * 3rd spin * 4th spin * 5th spin * 6th spin * 7th spin * 8th spin * 9th spin

Probability = (5/5) * (5/5) * (5/5) * (5/5) * (5/5) * (5/5) * (5/5) * (5/5) * (1/5)

Probability = 0.2

There is a 20% chance to get brown on the last spin.