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 Yllow Red OrangeGre en Blue 10% Brown 10% Percentage 17% 2390 2390 9% 8% 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 not possible Yes. 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? No. 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 Yes. Choosing a yellow and red M&M is not possible (c) Find P(not purple candy)

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Answer #1

Form the bag we have to choose only one candy. That can be either blue or green, but not both blue and green so

P(green\; \; or\; \; blue)=P(green)+P(blue)=0.08+0.1=0.18

Yes, these outcomes are mutually exclusive because choosing a blue and green M&M is not possible.

Similarly, the one candy we choose can be either yellow or red. Then,

P(yellow\; \; or\; \; red)=P(yellow)+P(red)=0.23+0.23=0.46

Yes, these outcomes are mutually exclusive because choosing a red and yellow M&M is not possible.

By the compliment law

P(not\; purple\; candy)=1-P(purple\; candy)=1-0.17=0.83

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