Interpreting IntersectionsDate: 07/09/2002 at 00:57:24 From: Jay Bunag Subject: Intersection of Sets Hi Dr. Math, I have been struggling with this Math problem from my brother. The problem is written below. Given that there are 100 people in the universal set. 10 people drink Coke, 15 drink Sprite, and 20 drink Pepsi. How many people are drinking both Coke and Pepsi at the same time? Coke and Sprite? Sprite and Pepsi? All three drinks? I tried getting the percentages and multiplying them to get the intersections. Is this the right way to do it? Thanks, Jay Date: 07/09/2002 at 12:55:23 From: Doctor Peterson Subject: Re: Intersection of Sets Hi, Jay. Is there some extra information you left out? First, there probably are NO people drinking both Coke and Pepsi at the same time; that would require two straws and peculiar taste. I suspect you really mean, how many people LIKE (that is, are _willing_ to drink) both Coke and Sprite. But there is no way of knowing that without further information. There might be 10 who drink ONLY Coke, 15 who drink ONLY Sprite, and 20 who drink ONLY Pepsi (and 55 who drink nothing): __10__ ____15____ ______20______ ____________55____________ / \/ \/ \/ \ | Coke | Sprite | Pepsi | nothing | \______/\__________/\______________/\__________________________/ Or there may be 10 who drink ANYTHING, 5 who drink anything EXCEPT Coke, and 5 more who drink ONLY Pepsi, while 80 drink nothing: ______20______ _____________________80______________________ / Pepsi \/ \ | ____15____ | | |/ Sprite \ | | | __10__ | | | |/ Coke \ | | | |\______/ | | | |\__________/ | | \______________/\_____________________________________________/ Or there could be any combination in between. So we just don't have enough information. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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