Question

A spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow. If the pointer is spun three times, find the probability it will land on green every time.

Answer 1

Answer:

The probability it will land on green every time is $\frac{1}{27}$.

Step-by-step explanation:

We are given that a spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow.

The pointer is spun three times.

As we know that the probability of an event is described as;

  Probability of an event =  $\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}$

Here, the favorable outcome is that the spinner will land on green every time.

So, the number of green regions = 2

Total number of regions = 3(red) + 2(green) + 1(yellow) = 6 regions

Now, the probability it will land on green every time is given by;

        Probability =  $\frac{2}{6}\times \frac{2}{6}\times \frac{2}{6}$

                           =  $\frac{1}{3}\times \frac{1}{3}\times \frac{1}{3}$

                           =  $\frac{1}{27}$

Hence, the probability it will land on green every time is $\frac{1}{27}$.