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M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the...

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 19% 17% 22% 10% 6% 8% 18% 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? No. Choosing a green and blue M&M is possible. Yes. Choosing a green and blue M&M is not possible. Yes. Choosing a green and blue M&M is 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).

Math   Statistics-And-Probability   
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Answer #1

Color Purple Yellow Red Orange Green Blue Brown

Percentage 19% 17% 22% 10% 6% 8% 18%

(a)

P(green candy and blue candy) = 0

Yes. Choosing a green and blue M&M is not possible

So, the outcomes are mutually exclusive. As these outcomes are mutually exclusive,

P(green candy or blue candy) = P(green candy) + P(blue candy) = 0.06 + 0.08 = 0.14

(b)

P(yellow candy or red candy)) = 0

Yes. Choosing a yellow and red M&M is not possible.

So, the outcomes are mutually exclusive. As these outcomes are mutually exclusive,

P(yellow candy or red candy)) = P(yellow candy) + P(red candy) = 0.17 + 0.22 = 0.39

(c)

P(not purple candy) = 1 - P(purple candy) = 1 - 0.19 = 0.81

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