Question

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?
b) What is the probability that a Starburst package has no cherry pieces?
c) What is the probability P[F1] that all 12 pieces of your Starburst are the same flavor

Answer 1

a) The probability that a Starburst package has only berry or cherry pieces and zero orange or lemon pieces is 1/6. b) The probability that a Starburst package has no cherry pieces is 5/6. c) The probability P[F1] that all 12 pieces of your Starburst are the same flavor is (1/4)^11.

Step-by-step explanation:

a) The probability of getting only berry or cherry pieces in a single Starburst is 2/4 = 1/2 (since there are four flavors). The probability of this happening for all 12 pieces is (1/2)^12 = 1/2^12 = 1/4096. Therefore, the probability of having only berry or cherry pieces and zero orange or lemon pieces is 1/6.

b) The probability of not getting a cherry in a single piece is 3/4. The probability of this happening for all 12 pieces is (3/4)^12 = 531441/248832. Therefore, the probability of having no cherry pieces is 1 - 531441/248832 = 181391/248832 ≈ 5/6.

c) The probability P[F1] that all 12 pieces are the same flavor is (1/4)^11 since the first piece can be any flavor, and the subsequent 11 pieces must match the first one. Hence, P[F1] = (1/4)^11.