I roll 12 4-sided dice. What is the probability that I roll at least one 2? What is the probability that I roll exactly three 2s?
So i take it, on any give roll, the probability of rolling a 2 is .25 (25%); the probability of rolling something else must be .75
The probability of rolling at least one 2 is: one minus the probability of never rolling a two. And, with 12 chances, that probability is .75^12
To calculate the probability of rolling exactly three 2s, first count the numbe of ways can happen. That is, calculate 12-choose-3. This will be (10*11*12)/(1*2*3) = 220. So, the probability of rolling exactly three 2s will be 220*(.75^9)*(.25^3) = 25.8%
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