Question

please double check work and round to four decimal places, fifth time posting.

A pharmacist receives a shipment of 22 bottles of a drug and has 4 of the bottles tested. If 6 of the 22 bottles are contaminated, what is the probability that no more than 1 of the tested bottles is contaminated? Express your answer as a fraction or a decimal number rounded to four decimal places

Answer 1

Number of bottles received = 22

Number of contaminated bottles = 6

Number of non-contaminated bottles = 22 - 6 = 16

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

P(no more than 1 of the tested bottles is contaminated) = P(0 contaminated bottles) + P(1 contaminated bottle)

= Number of ways in which 4 bottles can be selected from 16 non-contaminated bottles/Number of ways in which 4 bottle can be selected from total 22 + (Number of ways in which 3 bottles can be selected from 16 non-contaminated bottles x Number of ways in which 1 bottle can be selected from 6 contaminated ones)/Number of ways in which 4 bottle can be selected from total 22

= 16C4/22C4 + 16C3 x 6C1/22C4

= (16C4 + 16C3 x 6)/22C4

= (1820 + 560x6)/7315

= 0.7081