In: Statistics and Probability
The Masterfoods Company says that yellow candies make up 20% of their plain M&M’s, red another 20%, and orange, blue, and green each make up 10%. The rest are brown.
a. If you randomly pick two M&M’s, what’s the probability that they are both brown? Round to TWO digits beyond the decimal.
b. If you randomly pick two M&M’s, what’s the probability that exactly one of the two is yellow? Round to TWO digits beyond the decimal.
c. If you randomly pick three M&M’s, what’s the probability that the third one is the first one that’s red?Round to THREE digits beyond the decimal.
d. If you randomly pick three M&M’s, what’s the probability that none are yellow? Round to THREE digits beyond the decimal.
e. If you randomly pick four M&M’s, what’s the probability that at least one is green? Round to THREE digits beyond the decimal.
A) P(brown) = 1 - (0.2+0.2+0.1x3)
= 0.3
P(both are brown) = 0.3x0.3 = 0.09
B) P(yellow) = 0.2
P(not yellow) = 0.8
P(exactly one yellow) = 2C1 x 0.8 x0.2 = 0.32
C) P(red) = 0.2
P(third one is the first red) = 0.8x0.8x0.2 = 0.128
D) P(not yellow) = 0.8
P(none of the three are yellow) = 0.8x0.8x0.8 = 0.512
E) P(green) = 0.1
P(not green) = 0.9
P(at least one green) = 1 - P(all 3 are not green)
= 1 - 0.9x0.9x0.9
= 0.271