Using Tables to Find Probabilities
Date: 10/23/2003 at 21:35:35 From: Dominic Subject: second grade probability problem Levi has 3 blue shirts and 1 red shirt. He has 1 pair of white slacks and 1 pair of blue slacks. The probability that he will wear white slacks and a blue shirt is ________ out of _________. I would think that you have BS BS BS RS WS BS Is the answer 3 out of 4?
Date: 10/25/2003 at 12:11:44 From: Doctor Ian Subject: Re: second grade probability problem Hi Dominic, Here's one way to think about it. Let's make a table, with the slacks along one side, and the shirts along the other: slacks white blue blue ? ? shirts blue ? ? blue ? ? red ? ? In each location of the table, we can write down what combination he's got, if he chooses the corresponding colors. For example, if he chooses a red shirt and white slacks, we get slacks white blue blue ? ? shirts blue ? ? blue ? ? red RW ? Does that make sense? Filling in the table, slacks white blue blue BW BB shirts blue BW BB blue BW BB red RW RB So there are 8 possible ways that things can go, some of which look the same. (For example, there are 3 ways that he might choose a blue shirt and white slacks.) The probability of a thing happening is defined this way: The number of ways the thing could happen probability = --------------------------------------------- The number of ways that anything could happen We know that there are 8 possible ways for anything to happen. And there are 3 possible ways for him to end up with a blue shirt and white slacks. So the probability of choosing a blue shirt and white slacks is 3 probability = - 8 (Note that this assumes he's going to choose randomly, e.g., by grabbing items without looking for them.) What's confusing about this is that if you just list the combinations that look different, there are only four: BW: blue shirt, white slacks BB: blue shirt, blue slacks RW: red shirt, white slacks RB: red shirt, blue slacks So it would be easy to think that the probability of BW should be 1 out of 4. But that's why we make the table--to take into account that the numbers of items of different colors aren't the same. To see why this is important, imagine that he's got one blue shirt, and a million red shirts. Surely the probability of ending up with a blue shirt isn't going to be 1 in 4! Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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