Probability of Two Dice Summing to 5Date: 09/22/2001 at 20:41:31 From: Yuxiao Subject: Probabilities I don't really understand how to do probabilities. For example: If a person rolls two dice, what is the probability of getting a five as the sum of the two dice? Can you explain it step by step? Date: 09/23/2001 at 07:33:40 From: Doctor Mitteldorf Subject: Re: Probabilities Dear Yuxiao, It takes a lot of getting used to. The only way to get a feeling that you really understand probabilities is to do lots and lots of examples. One important principle is multiplication. You're familiar with multiplying numbers like 7*3 = 21, where the numbers get bigger as you multiply them. But if the numbers are fractions less than 1, then multiplying them together makes the result smaller. All probabilities are less than or equal to 1, so multiplying them together makes a smaller number. If the probability of one thing happening is x and the probability of another thing happening is y, you can multiply x times y to get a smaller number that is the probability of both things happening. Let's apply this to the two dice. You know that the probability of getting a 1 on the first die is 1/6. The probability of getting a 4 on the second die is also 1/6. So multiply these two together and you find that the probability of getting BOTH a 1 on the first die AND a 4 on the second die is 1/36. That's one of the ways you can get a 5 with two dice. So 1/36 is part of the probability of rolling a 5, but not all of it. Can you list the other ways? First die Second die 1 4 2 3 3 2 4 1 We've listed four ways to get a five, and that's all there are. Each of these combinations has a probability of 1/36 of happening; so the total probability of rolling a 5 is 4/36, which is 1/9. A good next step for you would be to make a chart of all the results 1 through 12 and calculate the probabilities for each in the way I just did for 5. You can check your chart when you're finished by adding up the probabilities for all 12 numbers: The probabilities should add up to 1. That's because one of these numbers HAS TO come up, so the probability of getting any number 1 through 12 is 1. - Doctor Mitteldorf, The Math Forum http://mathforum.org/dr.math/ Date: 09/23/2001 at 07:47:13 From: Doctor Anthony Subject: Re: probabilities In your example, the probability is the ratio Number of ways we can get a total of 5 -------------------------------------- Total number of possible outcomes From here you simply count the ways we can get 5. 1 + 4 probability of this is (1/6)(1/6) = 1/36 2 + 3 " " = 1/36 3 + 2 " " = 1/36 4 + 1 " " = 1/36 -------------- Total probability = 4/36 = 1/9 Alternatively, there are 4 ways we can get a total of 5 and there are 36 possible outcomes when you roll two dice. 4 1 Required probability = ----- = --- 36 9 - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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