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 !
In: 12
There are definitely formulas to work this out, but to me the easiest way is to do the opposite. What are the chances none of them are 6?
5/6 chance that any individual dice is not a 6. So the chance none are 6 is (5/6)^6 =0.335. therefore the chance at least 1 is a six is 1-0.335 = 0.665. or 66.5% chance.
Which obviously isn’t the same as 100%, which may not be what many people would first think!
You can repeat with as many dice as you want. Formula would still be 1-(5/6)^x where X is number of dice (or number of rolls, if you just reroll a single dice). You’ll note that as x gets larger the answer gets larger, but will never reach 1 as it’s still not a guarantee that you’ll ever get a 6.
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