Question

In: Statistics and Probability

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 23%, Yellow 19%, Red 22%, Orange 9%, Green 6%, Blue 6%, Brown 15%

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?

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

B. No. Choosing a green and blue M&M is not possible.    

C. Yes. Choosing a green and blue M&M is possible.

D. No. Choosing a green and blue M&M is possible.

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

Are these outcomes mutually exclusive? Why?

A. Yes. Choosing a yellow and red M&M is possible.

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

C. No. Choosing a yellow and red M&M is not possible.

D. No. Choosing a yellow and red M&M is possible.

(c) Find P(not purple candy).

Solutions

Expert Solution

Solution:

Given:

Color Percentage
Purple 23%
Yellow 19%
Red 22%
Orange 9%
Green 6%
Blue 6%
Brown 15%

Part a) Find P(green candy or blue candy).

P(green candy or blue candy) = P(green candy) + P(blue candy)

P(green candy or blue candy) = 6% + 6%

P(green candy or blue candy) = 12%

P(green candy or blue candy) = 0.12

Are these outcomes mutually exclusive? Why?

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

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

P(yellow candy or red candy) = P(yellow candy) + P(red candy)

P(yellow candy or red candy) = 19%+ 22%

P(yellow candy or red candy) = 41%

P(yellow candy or red candy) = 0.41

Are these outcomes mutually exclusive? Why?

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

Part c) Find P(not purple candy).

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

P(not purple candy) =1 - 0.23

P(not purple candy) = 0.77

orchestra answered 2 years ago
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