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 21% 18% 18% 8% 8% 6% 21%
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).

Are these outcomes mutually exclusive? Why?
Yes. Choosing a green and blue M&M is possible.
No. Choosing a green and blue M&M is possible.
Yes. Choosing a green and blue M&M is not possible.
No. Choosing a green and blue M&M is not possible.


(b) Find P(yellow candy or red candy).

Are these outcomes mutually exclusive? Why?
Yes. Choosing a yellow and red M&M is possible.
Yes. Choosing a yellow and red M&M is not possible.
No. Choosing a yellow and red M&M is possible.
No. Choosing a yellow and red M&M is not possible.


(c) Find P(not purple candy).

Answer 1

Since the Σ( of all colors )= 100%,  OR 1, then:

a) P(GREEN ∪ BLUEU) = P(G) + P(BL) = 8%+6% = 14% or 0.14

Since we have to choose ONE candy and only ONE candy at random, then tey are mutually exclusive: No. Choosing a green and blue M&M is possible

b) P(YELLOW ∪ RED) = P(Y) + P(R) = 18%+18% = 36% or 0.36
SAME ANSWER AS BEFORE: mutually exclusive

c) P(NOT PURPLE), Let's calculate 1st, the probability of having a PURPLE:
P(PURPLE) = 21% or 0.21
And the Probability of NOT having a PURPLE is 1-0.21 = 0.79