SOLUTION: suppose a person rolls a die 5 times and gets a 5 every single time. Suppose the die is rolled a sixth time, what is the probability that another 5 comes up?
I figured the sixth
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-> SOLUTION: suppose a person rolls a die 5 times and gets a 5 every single time. Suppose the die is rolled a sixth time, what is the probability that another 5 comes up?
I figured the sixth
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Question 603313: suppose a person rolls a die 5 times and gets a 5 every single time. Suppose the die is rolled a sixth time, what is the probability that another 5 comes up?
I figured the sixth die would be 1 out of 6. The answer seems too easy. I'm horrible in math so when an answer seems too easy, usually it's wrong. Found 2 solutions by bucky, scott8148:Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! You are wrong if you think you are horrible at math. You have good intuition.
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On the sixth roll, the probability of rolling a 5 IS 1 out of 6, just as it would be on any single roll.
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What is confusing about this is the thought that you are going for six fives in a row. What are the chances of rolling six fives in a row? You feel that it is not very likely that you would be able to do it. But you have already successfully completed a very hard part ... namely you have already rolled five fives in a row, so you can forget doing that hardest part.
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To get five fives in a row, you have a 1 in 6 chance of getting a 5 in each roll. So by multiplying 1 in 6 (or 1/6) by itself 5 times you get:
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That is equivalent to:
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and is equal to 7776. This means that you have 1 chance is 7776 of getting five fives in a row.
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To start from the beginning and calculate your chances of rolling six fives in a row, you would calculate:
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and this multiplication is equivalent to:
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which is 1 in 46656.
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As I said earlier, a lot of the confusion is caused because of the sense that it is very difficult (a 1 in 46656 chance) of rolling six fives in a row. But when you have already managed to get five successive rolls of a five, you have already completed a very difficult portion of that chance in that you have already accomplished something that you have only a 1 in 7776 chance of doing. Once you have successfully reached that point you then have a 1 in 6 chance of completing the sixth five in a row.
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In this case, you were right in your "common sense" solution. It may seem too easy, but that is the point of the exercise ... to help you understand that each separate roll has the same probability of achieving "success" ... meaning a 1 in 6 chance of getting a specific number.
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Hope this helps you to understand why your intuition was exactly correct.
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