If 18 car owners are randomly selected, find the probability that at most two people have their cars washed professionally.

Question

A study found that 28% of car owners in America had their cars washed professionally rather than do it themselves. If 18 car owners are randomly selected, find the probability that at most two people have their cars washed professionally.

Answer 1

28% or .28 = Probability that a car was washed professionally rather than do it themselves.

72% or .72 = Probability that a car was not washed professionally rather than do it themselves.

Because 28% + 72% = 100%

₁₈C₀(.72)¹⁸ = The probability that none of the 18 cars were washed professionally.

₁₈C₁(.72)¹⁷(.28) = The probability that exactly one of the 18 cars were washed professionally.

₁₈C₂(.72)¹⁶(.28)² = The probability that exactly two of the 18 cars were washed professionally.

₁₈C₀(.72)¹⁸ + ₁₈C₁(.72)¹⁷(.28) + ₁₈C₂(.72)¹⁶(.28)² ≈ 0.0842 or 8.42%