Question

A pharmacist receives a shipment of 15 bottles of a drug and has 5 of the bottles tested. If 6 of the 15 bottles are contaminated, what is the probability that at least 4 of the tested bottles are contaminated? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Let

number of bottles = 15

p = proportion of bottles are contaminated = 6/15 = 0.40

We asked to find probability that at least 4 of tested bottles are contaminated if 5 bottles are selected

P( X 4 ) = P( X = 4 ) + P( X = 5)

Using binomial probability

n = 5 , p = 0.40

P( X = 4 ) = 5!/4!*1! * (0.40)⁴*(0.60)¹ = 0.0768

P( X = 5) = 5!/5!*0! *(0.40)⁴*(0.60)⁰ = 0.0102

P( X 4) = 0.0768 + 0.0102

P( X 4 ) = 0.0870