Probability of the same thing happening 16 out of 19 times?
I'm not very good at statistics but I was hoping someone could help me out finding the probability of something. Essentially, I rolled a 9-sided die 19 times, and 16 of the rolls were the same number. What is the probability of this?
2011-04-12T14:19:21Z
This didn't actually have anything to do with a die, I was just using that as an example. I did something which had nine outputs - equally probable - 19 times. 16 of those times I got the same output. Thanks for the help.
Anonymous2011-04-12T14:22:49Z
Favorite Answer
You may or not know the formula for probability is: P(x=r) = (n!/(r! * (n-r)!)) * (P^r) * (Q^(n-r)) P(x=r) = nCr * (P^r) * (Q^(n-r))
where n is the total number of attempts (19 in your case), P is the probability of getting the outcome (1/9 in your case), Q is the probability of not getting the outcome (8/9 in your case), and r is the amount of times out of the total your looking for the probability of.
You need to calculate the value of: P(X=16) <-- meaning the probability (P) of the outcome (X) happening 16 times
If every side has a different number on it, and each side has the same probability of being rolled, the probability of EXACTLY 16 rolls the same would be:
9 * 19! / (16! * 3!) * (1/9)^16 * (8/9)^3 = 3.3* 10^-12: about 1 in 300 blion
However - I don't know of any evenly weighted 9-sided dice. Are you sure this isn't a TEN-sided die, with numbers 0-9? The odds would be a little worse then - about 1 in 2 trillion.
You would have been better off choosing an even amount of times to roll like 20, because 19 doesn't go into 100, meaning if you wanted a percent, that's impossible. If you want a fraction, the only one possible is16/19 because 19 is prime, and it can't be simplified.