What is the probability that at most 4 people have a dog? Round your answer to the nearest hundredth.

Question

According to a survey, about 45% of people ages 18 and older in a city have a dog. You ask 6 randomly chosen people (ages 18 and older) whether they have a dog.

Answer 1

P(k≤4) = ∑_i=0⁴P(k=i); p = 0.45, q = 1 - p = 0.55; P(k = i) = C(n,i)pⁱq^n-i, n = 6

P(k≤4) = C(6,0)·0.45⁰·0.55⁶ + C(6,1)·0.45·0.55⁵ + C(6, 2)·0.45²·0.55⁴ + C(6, 3)·0.45³·0.55³ +

C(6, 4)·0.45⁴·0.55² = 0.930802