Question

M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the distribution of colors for plain M&M candies is as follows.

Color Purple Yellow Red Orange Green Blue Brown
Percentage 17% 18% 17% 7% 6% 10% 25%

Suppose you have a large bag of plain M&M candies and you choose one candy at random.

a. Find P(green candy or blue candy).
b. Are these outcomes mutually exclusive? Why?

Answer 1

`P(Green\ candy\ or\ Blue\ candy) = 0.16`

Yes, they are mutually exclusive

Explanation:

Given

Refer to the table in the question

Solving (a): P(green candy or blue candy)

This is calculated as:

`P(Green\ candy\ or\ Blue\ candy) = P(Green) + P(Blue)`

From the question:

`P(Blue) = 10\%`

`P(Green) = 6\%`

So:

`P(Green\ candy\ or\ Blue\ candy) = P(Green) + P(Blue)`

`P(Green\ candy\ or\ Blue\ candy) = 6\% + 10\%`

`P(Green\ candy\ or\ Blue\ candy) = 16\%`

Convert to decimal

`P(Green\ candy\ or\ Blue\ candy) = 0.16`

Solving (b): Are they mutually exclusive?

Multiple events A and B are mutually exclusive if;

`P(A\ or\ B) = P(A) + P(B)`

In (a) above:

`P(Green\ candy\ or\ Blue\ candy) = P(Green) + P(Blue)`

and this is so every other possible colour of candy

e.g.

`P(Red\ or\ Yellow) = P(Red) + P(Yellow)`

Hence:

The events are mutually exclusive