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A Starburst candy package contains 12 individual candy pieces. Each piece is equally likely to be berry, orange, lemon, or cherry, independent of all other pieces. (a) What is the probability that a Starburst package has only berry or cherry pieces and zero orange or lemon pieces

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Answer:

(a) Each piece is “berry or cherry” with probability p = 1/2. The proba-

bility of only berry or cherry pieces is p

12 = 1/4096.

Step-by-step explanation:

(b) Each piece is “not cherry” with probability 3/4. The probability all 12

pieces are “not pink” is (3/4)12 = 0.0317.

(c) For i = 1, 2, . . . , 6, let Ci denote the event that all 12 pieces are flavor i.

Since each piece is flavor i with probability 1/4, P[Ci

] = (1/4)12. Since

Ci and Cj are mutually exclusive,

P[F1] = P[C1 ∪ C2 ∪ · · · ∪ C4] = X

4

i=1

P[Ci

] = 4 P[C1] = (1/4)11

.

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