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
The problem with the 1/6 + 1/6 approach (for two dice) is that the particular situation where you roll a pair of sixes is counted twice. You counted it in the first 1/6 and also in the second 1/6. This smidgen of probability needs to be removed from one of the 1/6’s to get an accurate total probability. (Picture a Venn diagram with two intersecting circles and you want the total area; you must not count the center area twice.) With many dice there are even more of these multiple six situations that were counted multiple times and must be removed. That makes your additive approach complicated. Feasible but complicated. It happens to be easier to figure out everything that doesn’t involve any sixes and then take 1 minus that.
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