Question

All three sections of the spinner below are equal in size. Andy sound the spinner three timesWhat is the probability the spinner will land on a different color?A) 1/27B)2/9C)1/3D)3/3

Answer 1

On this question we want to find the probability that Andy spins the wheel three times and obtain three different collors. For this we first need to understand the probability of the spinner stopping on any of the three given colors, since they are all the same size the probability for each color must be the same. There are three colors, so the probability is:

`p(1\text{ color)=}(1)/(3)`

We want to find the probability of three consecutive spins to land on three different collors. Since each spin is independent from each other, then the probability is given by:

`p=p(\text{yellow)}\cdot p(\text{blue)}\cdot p(\text{red)}`

Each of these is equal to one third.

`p=(1)/(3)\cdot(1)/(3)\cdot(1)/(3)=(1)/(27)`

The correct answer is A 1/27.