Question

A pharmacist receives a shipment of 20 bottles of a drug and has 4 of the bottles tested. If 4 of the 20 bottles are contaminated, what is the probability that exactly 3 of the tested bottles are contaminated? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Answer:

given that:

A pharmacist receives a shipment of 20 bottles of a drug and has 4 of the bottles tested. If 4 of the 20 bottles are contaminated.

There are total 20 bottles.

=(20-4)

=16

16 bottles are pure.

Let X be the number of bottles are contaminated.

probability that exactly 3 of the tested bottled are contaminated is

Total probability =20C3

=1140

probability exactly 3 of tested are contaminated is

=4C2*16C1+4C3*16C0+4C1

=6*16+4*1+4

=96+4+4

=104

probability that bottles are contaminated=104/1140

0.0912

probability that exactly three bottles are contaminated=0.0912.