A study determined that 9 of persons age 65 to 74 have a cer

A study determined that 9% of persons age 65 to 74 have a certain symptom. A group of 16 persons age 65 to 74 are selected at random. Find the probability that at most 1 person has the symptom.

Solution

Probability of getting 1 person with symptom = 9% =0.09

Probability of getting 1 person without symptom = 1- 0.09 = 0.91

Required probability = probability of getting no person with symptom + probability of getting only one person with symptom

= 16C₀ (0.09)⁰ (0.91)¹⁶  + 16C₁ (0.09)¹ (0.91)¹⁵ = 0.221 + .35=0.571(answer)