The spinners alongside are each spun once. Find the probability that the spins are the same, colour.

Answer 1

As your commenter said, you do not have specifics. So, I will make up a simple scenario:

Say we have two spinners side-by-side. Each of the teo spinners have three colors on them: Red, Blue and Yellow.

what is the probability after spinning each spinner once, that each spinner stops on the same color?

Some background:

Note that each spin is an independent event (one event does not affect the other). So, for one spinner, the probability of getting Yellow is 1/3, and of course this holds true for the other spinner as well, 1/3 for getting yellow.

Since each spin is independent, and we are asking the probability of Yellow AND Yellow, we take each of the probabilities and multiply them together. The operative word is AND which indicates us to multiply:

1/3 times 1/3 = 1/9 for each getting Yellow

For getting both Blue:

1/3 times 1/3 = 1/9

Fir getting both Red:

1/3 times 1/3 = 1/9

Notice the nine possible outcomes are:

Blue and Blue

Blue and Red

Blue and Yellow

Red and Red

Red and Blue

Red and Yellow

Yellow and Yellow

Yellow and Blue

Yellow and Red

Ultimately, the question is that they each end with the SAME color. So, it becomes either both end in Yellow OR both end in Red OR both end in Blue. OR indicates to us to ADD the probabilities:

So, 1/9 + 1/9 + 1/9 = 3/9 = 1/3

Also, this matches with the probability of three out of nine in the detailed outcomes above =>. 3/9 = 1/3

So, 1/3 is the final answer for this particular problem.

If your teacher is requesting you to generalize this answer into the unspecific question you asked, it goes as follows:

For n spinners, each with m colors equally probable, and we want each to end with the same color, the probability if this occurring is:

probability = n[1/nm)] = 1/m

I hope this helps! :-)