Question

An internet research company surveyed 90 online shoppers, each of whom made one purchase today. The company recorded the type of purchase each shopper made. Here is a summary. Type of purchase Number of shoppers Beauty supplies 12 Clothing 33 Pet supplies 21 Office supplies 24 Three shoppers from the survey are selected at random, one at a time without replacement. What is the probability that none of the three shoppers purchased beauty supplies? Do not round your intermediate computations. Round your final answer to three decimal places.

Answer 1

Here, we are given the following data:-

Type of Purchase	Number of Shoppers
Beauty Supplies	12
Clothing	33
Pet Supplies	21
Office Supplies	24
Total	90

n= 90 total online shoppers.

And we have to select 3 shoppers at random without replacement.

This can be done in

ways.

Now, we have to obtain the probability that none of the three shoppers purchased Beauty supplies.

i.e. P(no Beauty supplies)

We will get all three non Beauty supplies only if we select from the other types of purchase, without considering Beauty supplies.

Notice that, there are such (33+21+24)= 78 shoppers.

Or (n - beauty supplies shoppers)= (90-12)= 78 shoppers.

Now, we have to select 3 shoppers from these 78 shoppers.

This can be done in

ways.

Hence,

Hence, the probability that none of the three shoppers purchased beauty supplies is 0.648

This answers your question.

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