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A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row? How do you solve this type of question for variable number of throws and number of repeats?

Teodor Dyakov
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  • Hint: How many possible outcomes are there for the 1000 rolls? What is the probability of getting 5 in a row the same? Now you just need to compute all possible ways of getting 5 in a row for 1000 rolls and divide that by the number of possible outcomes. – layabout Oct 14 '20 at 16:01
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    You should wait before asking cross-sites https://stats.stackexchange.com/questions/492000/a-fair-die-is-rolled-1-000-times-what-is-the-probability-of-rolling-the-same-nu – Anindya Prithvi Oct 15 '20 at 07:16

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How to calculate the probability of rolling 6 at least 5 times in a row, out of 50 tries?

This question is very similar to yours. You have to modify it for not having exactly the number 6 but the same number, so you will have different probabilities. Try calculating it for one specific number and then expand your approach.

samabu
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  • You can not just calculate it for a specific number and then multiply it or something like that. Instead, you can use the fact that rolling any number $k$ times in a row in $n$ tries, is similar to rolling a specific number $k-1$ time in a row in $n-1$ tries. You can see it as tracking whether the dice rolls the same number as the one before (which has 1/6-th probabilty) and this $k-1$ times. – Sextus Empiricus Oct 17 '20 at 12:19