Question

a pharmacist receives a shipment of 15 bottles of a drug and has 4 of the bottles tested. if 4 of the 15 bottles are contaminated, what is the probability that more than 1 of the tested bottles is contaminated? round to 4 decimal places

Answer 1

Probability of a contaminated bottle = 4/15

Let X be the number of contaminated bottles selected among the 4 of the bottles tested. Then X ~ Binomial(n = 4, p = 4/15)

Probability that more than 1 of the tested bottles is contaminated = P(X > 1)

= 1 - P(X 1)

= 1 - [P(X = 0) + P(X = 1)]

= 1 - [⁴C₀  * (4/15)⁰ *  (1 - 4/15)^4-0  + ⁴C₁  * (4/15)¹ *  (1 - 4/15)^4-1 ]

= 1 - [ (11/15)⁴ +  4  * (4/15) *  (11/15)³ ]

= 1 - (0.2892  + 0.4207)

= 0.2901