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:
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.
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