<p>Hey guys, I'm just reviewing the probability problems and rules, and they are a nightmare. I'm reviewing some problems in the Dr. Chung book for example, and it would be great if you could help me out: (Oh is there an SAT probability guide somewhere in CC?)</p>
<p>If a fair die is thrown three times, what is the probability that a 5 comes up exactly two times?</p>
<p>I thought is was (1/6)(1/6)(5/6), but then the book says (1/6)(1/6)(5/6)(3)=5/72. I kind of get it, but its really confusing. </p>
<p>Thanx.</p>
<p>The probability of the first two dice being 5’s and the last not being a 5 is (1/6)(1/6)(5/6), and I assume you understand this much? The probability of the first and last dice being 5’s and the second not is (1/6)(5/6)(1/6). The same concept applies to the last two dice being 5’s. (5/6)(1/6)(1/6). Now add all three of these equations together to get the final answer. It simplifies to (1/6)(1/6)(5/6)(3). Does this help? I’m not always so good at explaining…</p>
<p>Um here’s a simpler example:</p>
<p>What’s the probability of rolling two dice and only one is a six?</p>
<p>There’s 36 different combinations. When the first one is a six, the second can be a 1, 2, 3, 4, or 5 (5 combinations). When the second is a six, the first can only be a 1, 2, 3, 4, or 5 (5 more combinations). This is 10 combinations out of 36, or 10/36.</p>
<p>Now let’s use the formula: (1/6)(5/6)(2) = 10/36</p>
<p>Pretty much what the first guy said, this actually isn’t very hard.</p>
<p>The probability it will be a five the first time ( 1 / 6 )</p>
<p>The probability it will be a five the second time ( 1 / 6 )</p>
<p>The probability it will NOT be a five the third time ( 5 / 6 )</p>
<p>Remember, you must not only take into consideration if it will happen, but also if it won’t happen. And of course, it could be a five the first, second, or third time.</p>
<p>Multiply : (1/6) * (1/6) * (5/6) = (5/72)</p>
<p>Oops typo ^ You meant to include the 3 in your equation, right? Because that was probably the hard part about this problem. By the way, I’m a girl :)</p>