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| Math Central | Quandaries & Queries |
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Question from Reane, a parent: 6 purple and 4 orange socks. Choose one then choose a second without putting the 1st back. What is the probability of getting 2 purple socks. I can't reach back far enough in my memory to recall how to do this. |
Hi Reane,
You have 6 purple and 4 orange socks in the drawer, for a total of 10 socks.
You pull one sock out at random, so it makes sense that you have a 6/10 chance of pulling out a purple one and a 4/10 chance of pulling out an orange one. Now there are 9 socks left in the drawer.
If you pulled an orange sock out, you can't have 2 purple socks, so you're finished.
If you pulled a purple sock out, there are 5 purple socks and 4 orange socks left in the drawer. You pull another one out at random, so it makes sense that on that pull, you have a 5/9 chance of pulling out a purple one and a 4/9 chance of pulling out an orange one.
So you have a 6/10 chance, and a 5/9 chance. To combine these, multiply the two fractions together, and you have your total probability. (6/10)x(5/9) = (30/90) = 1/3 chance of getting 2 purple socks.
Hope this helps!
Gabriel
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