39. M&M;\'s The Mars company says that before the intro- duction of purple, yell

Question

39. M&M;'s The Mars company says that before the intro- duction of purple, yellow candies made up 20% of their plain M&M;'s, red another 20%, and orange, blue, and green each made up 10%. The rest were brown. a) If you pick an M&M; at random, what is the probabil- ity that 1. it is brown? 2. it is yellow or orange? 3. it is not green? 4. it is striped? b) If you pick three M&M;'s in a row, what is the prob- ability that 1. they are all brown? 2. the third one is the first one that's red? 3. none are yellow? 4. at least one is green?

Explanation / Answer

Suppose we have 100 candies in total. Then

yellow=20,red=20,orange=10,blue=10,green=10,brown=30

a) If you pick an M&M at random, the probability that

1) it is brown is 30/100 ie 0.3

2) it is yellow or orange is (20+10)/100 ie 0.3

3) it is not green is 0.9

P(not green)=1-probability it is green=1-10/100=1-0.1= 0.9

4)it is striped is 0 as all candies are all single colored candies.

b) If you pick three M&M's in a row, what is the probability that

1) they are all brown 30C3/100C3 = 4060/161700 = 0.025108

2)the third one is the first one that's red

(20/100)*(99/99)*(19/98) = 0.0387

3) none are yellow = 1- P(all yellow) = 1-(20/100) = 1-0.2 = 0.8

4)at least one green = 1- P( pick all other colour ) = 1- (99C2/100C3) = 4851/161700 = 0.03

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