I swear I leaned this in school at some point but its been bothering me .
If you throw a six sided die, the odds of rolling a six are 1/6.
But what are the odds of rolling at least one six if you throw two dice at the same time? I thought it was 1/6 + 1/6 or 2/6, but suspect I might be wrong.
This is the idea that has me stuck. If you throw 6 dice at the same time what are the odds of rolling at least one 6 ? It can’t be 6/6 or 100%. The odds of rolling at least one 6 are certainly high but absolutely not 100%, so the logic I used for the two dice can’t be correct. There must be a formula for this but I’m having trouble searching for it . Thanks !
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There are two ways to solve this: either you can work out all possible permutations of six dice (there are 46,656 of them), count which ones have one or more sixes, and divide that by the total.
Or, you can calculate the odds that you roll zero sixes and take the opposite. This is the easier method: the odds of not rolling a six are 5/6. To find the probability that two independent events will occur, you multiply them. So if you have six dice, you should multiply 5/6 by itself six times, i.e. raise it to the sixth power. This is 15625/46656, or about 33%. That is the odds of rolling zero sixes, so the odds of rolling at least one six are 67%.
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