by tommywallach Mon Mar 03, 2014 11:24 pm
Hey Kwame,
Anytime a question mentions "at least," it means you're going to use the 1-x trick. This trick is based on the fundamental equation of probability:
P(Event Happening) + P(Event Not Happening) = 1
This is important because we could write the equation like this:
P(At least two people get the same thing) + P(Nobody gets the same thing as anyone else) = 1
Do you see that those two possibilities are ALL the possibilities? And this means we can get the answer by doing this:
P(At least two people get the same thing = 1 - P(Nobody gets the same thing as anyone else)
We do this because it's way easier to solve for P(Nobody gets the same thing as anyone else). To do that we just look at what we need everyone to roll
Person 1: 6/6 (this person can roll anything)
Person 2: 5/6 (this person needs to roll something different from person 1)
Person 3: 4/6 = 2/3 (this person needs to roll something different from both person 1 AND person 2)
Person 4: 3/6 = 1/2 (this person needs to roll something different from peoples 1, 2, and 3).
1 * 5/6 * 2/3 * 1/2 = 10/36 = 5/18
We're almost done. Go back to our original equation:
P(at least two people roll the same thing) = 1 - 5/18 = 13/18
Hope that makes more sense!
-t