Help with probability problem. So I saw this math problem on an internet forum a while ago and I decided to take a shot at it. The first way I tried it gave me a wrong answer. The second way gave me the correct answer. I've been trying to figure out why the first attempt was wrong when, logically, it should be equal. The problem went something like this. "You have a population of men and women. The chance of picking a single man is 1/3. If picking 2 men(without replacement) yields a probability of 1/10, how many people are in the population?" On the left is the correct way(my second attempt) to do it but the right is identical, only using decimals instead of fractions. So any idea why it doesn't work? Also, the bottom portion is a random attempt that got me another weird answer... Seriously, I've been racking my brain on this and just can't get it. My stats teacher was stumped as well so if anyone can help me out I would love you forever. =) 
Re: Help with probability problem. The attachement is unreadable. 
Re: Help with probability problem. How do you, for example, get .3(repeated]x.3(repeated) = .1(repeated)? Also, you can not divide out added terms from the numerator and denominator. The right side is just plain rubbish. You need to follow the rules of arithmetic and algebra. 
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Re: Help with probability problem. is equivalent to but is not equivalent to . 
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In your problem, there is no need to convert to decimals  if you must, though, note that This should give the correct answer. 
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For clarity in future, I'd recommend downloading and using MathType to write your formulas, showing clear steps to leave no doubt. You'll have to learn how to use it, but it does make a big difference. 
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