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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 17% 18% 17% 7% 6% 10% 25%

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).
b. Are these outcomes mutually exclusive? Why?

Sagot :

MrRoyal

Answer:

[tex]P(Green\ candy\ or\ Blue\ candy) = 0.16[/tex]

Yes, they are mutually exclusive

Step-by-step explanation:

Given

Refer to the table in the question

Solving (a): P(green candy or blue candy)

This is calculated as:

[tex]P(Green\ candy\ or\ Blue\ candy) = P(Green) + P(Blue)[/tex]

From the question:

[tex]P(Blue) = 10\%[/tex]

[tex]P(Green) = 6\%[/tex]

So:

[tex]P(Green\ candy\ or\ Blue\ candy) = P(Green) + P(Blue)[/tex]

[tex]P(Green\ candy\ or\ Blue\ candy) = 6\% + 10\%[/tex]

[tex]P(Green\ candy\ or\ Blue\ candy) = 16\%[/tex]

Convert to decimal

[tex]P(Green\ candy\ or\ Blue\ candy) = 0.16[/tex]

Solving (b): Are they mutually exclusive?

Multiple events A and B are mutually exclusive if;

[tex]P(A\ or\ B) = P(A) + P(B)[/tex]

In (a) above:

[tex]P(Green\ candy\ or\ Blue\ candy) = P(Green) + P(Blue)[/tex]

and this is so every other possible colour of candy

e.g.

[tex]P(Red\ or\ Yellow) = P(Red) + P(Yellow)[/tex]

Hence:

The events are mutually exclusive

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