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 23% 21% 19% 10% 7% 7% 13% 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. Yes. Choosing a green and blue M&M is not possible. No. Choosing a green and blue M&M is not possible. No. Choosing a green and blue M&M is possible. (b) Find P(yellow candy or red candy). Are these outcomes mutually exclusive? Why? Yes. Choosing a yellow and red M&M is not possible. Yes. Choosing a yellow and red M&M is 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

(a) P(green candy or blue candy)=14%

These outcomes are mutually exclusive. Choosing a green and blue M&M is not possible.

(b) P(yellow candy or red candy)= 40% These outcomes are mutually exclusive. Choosing a yellow and red M&M is not possible.

(c) P(not purple candy)=77%

Explanation:

To get the probability equally likely of having a candy we use the following formula

P=# of possibilities that meet the condition / #of equally likely possibilities.

In this case, we are consider 100 candies as the number of equally likely possibilities.

P(green candy or blue candy)

green candy= 7 candies over 100 ( 7 %)

blue candy= 7 candies over 100 ( 7 %)

P(green candy or blue candy)= 7+7 / 100= 14/100=14%

Are these outcomes mutually exclusive? Yes. Choosing a green and blue M&M is not possible. Both can't occur at the same time.

(b) P(yellow candy or red candy)

yellow candy= 21 candies over 100 ( 21 %)

red candy= 19 candies over 100 ( 19 %)

P(yellow candy or red candy)= 21+19 / 100= 40/100=40%

Are these outcomes mutually exclusive? Yes. Choosing a green and blue M&M is not possible.

(c) P(not purple candy)= to get this probability we have to consider the others possibilities, we can get Yellow, Red, Orange, Green, Blue or Brown,

that means 21+ 19+ 10+ 7+ 7+ 13=77

P(not purple candy)= 77/100= 77%