# how to calculate the probability of having more than X events with probability Px on Y attempts

I'm trying to figure out the formula to calculate the probability of having more than X events with probability Px on Y attempts.

For example if I use a dice with 10 faces, I toss it 100 times (y = 100) I would like to calculate the probability of the top face being a number equal or less than 4 (Px = 0.4) for more than 40 times (x = 40)

Update:

I need to place these results on an excel sheet, I've tried doing the following:

I8 contains the number of tosses (i.e. 100)
G8 contains the win ratio (i.e. 0.4)
S8 contains the number of successes (=I8*G8)
T8 number of failures (=I8*R8)
R8 probability of failure (=1-G8)

L8 Pmf: =(FACT(I8)/(FACT(S8)*FACT(T8)))*POWER(G8,S8)*POWER(R8,T8)
M8 the result I'm looking for: (=L8*I8)


For several values the result is higher than 1, which makes me wonder where's the problem, for example with values:

G8 0.4
I8 100
M8 the result ends up being approx 8.12....


I apologize for using Excel for doing math, but I need these results on a spreadsheet and for many different values, I'm not sure I have alternatives.

• well I'm not too poised in probability, I know how to calculate the probability of having exactly that number of outcomes: Nx = number of X; Nk = y - Nx; Pnx = (y)! / Nx! * Nk! * Px * Pk Commented Aug 4, 2014 at 16:24