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Cynthia represents AVON in her neighborhood. Cynthia’s children have been playing with the lipstick order and have mixed up the boxes and the contents so that the color of the lipstick in the box may not conform to the label on the box. There are 20 boxes in all and the children say that they only played with five of the boxes. Assuming that to be true, what is the chance that Cynthia has to open more than ten boxes to find all of the incorrectly labeled lipsticks? Why does the method of analysis for this question give us so little information of value?

Submitted: 123 days and 12 hours ago.

Category: Math

Value: $9

Status: CLOSED

Posted by muvee 123 days and 12 hours ago.

Info Request

please clearify:
Does children played 5 box mean that exact 5 box are incorrect?

Accepted Answer

Dear XXXXXXXXXX,

Great question! Here's how I'd answer it.

In this case, the probability of finding all 5 boxes is the same as finding none of the boxes at all. Choosing 10 of them divides the boxes into two groups. The probability of finding none of the boxes is:

15/2014/1913/1812/1711/1610/159/148/137/12*6/11 = 0.0163

So the probability that she finds all 5 boxes by searching the first 10 boxes is 0.163. So the probability that she has to look in more than 10 is 0.9837. In other words, she is most likely going to have to search through more than 10 of them.

This method of analysis is so challenging because the probabilities are so hard to figure out. Since there are so many boxes, the number of ways to select a particular number of boxes is quite difficult to calculate. Hence, it's difficult for us to determine the probabilities. This is the only one that we can calculate easily. So we can't get much information from this method.

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Let me know if you have questions about this. I'm happy to clarify any details!

Accepts:
Expert:	Greg
Pos. Feedback:	99.6 %
Answered:	7/21/2009

Graduate Student

I teach math and statistics at a college level as a graduate teaching assistant

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