Question 2 of 13, Step 1 of 1 Correct A pharmacist receives...

Question 2 of 13, Step 1 of 1 Correct A pharmacist receives a shipment of 18 bottles of a drug and has 3 of the bottles tested. If 3 of the 18 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.

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00:01 In this problem it is said that we have a shipment of 18 bottles of a drug.

00:05 5 of the bottles are tested.

00:07 4 of the 18 are contaminated and we want to find the probability that at least 3 of the tested bottles are contaminated.

00:14 So the required probability will be the number of favorable outcomes divided by the total number of outcomes.

00:19 First of all consider the total number of outcomes.

00:21 That will be the number of ways of selecting 5 bottles to be tested.

00:25 So out of the 18 bottles any 5 are selected at random.

00:28 This can be done in 18 c5 ways.

00:30 Here we use c which represents combination.

00:33 And we use combination and not permutation in this case because the order of selection of the bottles does not matter.

00:39 Next consider the number of favorable outcomes.

00:41 That will be the number of ways there are at least 3 bottles which are contaminated amongst the tested bottles.

00:47 So note that a total of 4 bottles are contaminated.

00:50 So there are 2 ways that we can have at least 3 bottles contaminated.

00:54 That is if we have exactly 3 bottles or if we have exactly 4 bottles contaminated.

01:00 So first of all let's consider the number of ways we can select 5 bottles so that exactly 3 are contaminated...

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