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).

Question

Mathematics

Valentino Rose

18 April, 14:50

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).

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Answers (1)

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Thalia Simmons · 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%

Step-by-step 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%