Conditonal Probability and Multipication Rules 1 Gneral Cand

Conditonal Probability and Multipication Rules:

1. Gneral: Candy colors M&M plain candies in various colors. According to the M&M /Mars Dept of Consumer Affairs, the distribution of colors for plain M&M candies is

COLOR Purple Yellow Red Crange Green Blue Brown

Percentage 20% 20% 20% 10% 10% 10% 10%

Suppose you have a large bag of plain M&M candies and you choose one candy at random . Find

(a) P9green candy or blue candy). Are these outcomes mutually exclusive?

(b) P(yellow cand or red candy). Are these outcomes mutually exclusive? Why?

(c) P(not purple candy)

Please explain...

Solution

(a)

We have following probabilties:

P(blue candy)=0.10

P(green candy)=0.10

Since you choose only one candy and candy can have only one color so the event selecting a green candy or selecting a blue candy are mutually exclusive. So

P(green candy or blue candy)=P(green candy)+P(blue candy)=0.10+0.10=0.20

(b)

We have following probabilties:

P(yellow candy)=0.20

P(red candy)=0.20

Since you choose only one candy and candy can have only one color so the event selecting a yellow candy or selecting a red candy are mutually exclusive. So

P(yellow candy or red candy)=P(yellow candy)+P(red candy)=0.20+0.20=0.40

(c)

P(purple candy)=0..20

By complement rule we have

P(not purple candy)=1-P(purple candy)=1-0.20=0.80