In a recent study 35 percent of people surveyed indicate chocolate was their favorite flavor of ice cream. Suppose we select a sample of ten people and ask them their favorite flavor.

Question

A: What is the probability that four or more name chocolate?

Answer 1

this is a binary probability ... chocolate (c) or not chocolate (n)
... p(c) = .35 ... p(n) = .65

(n + c)^10 = n^10 + 10 n^9 c + 45 n^8 c^2 + 84 n^7 c^3 + ... + c^10

sum the 1st four terms and subtract from 1
... 1 - [.65^10 + (10 * .65^9 * .35) + (45 * .65^8 * .35^2) + (84 * .65^7 * .35^3)]