Calculating a Binomial Probability
Finding :
In mathematics, to calculate the binomial probability, P(X = x), we use the formula . The TI83/84 has this formula already built in. The calculator function is binompdf (n, p, x).
To calculate P(X=3) given n = 4, p = 0.41, and q = 0.59, press 2nd VARS [DISTR], ARROW DOWN to select 0:binompdf(, and then press ENTER.



After binompdf( type 4,.41,3), and then press ENTER. See the results below.

To 4 decimal places, the P(X = 3) = 0.1627.
To calculate the probablity P(X x) by hand, we would have to calculate each individual probability, P(0), P(1), P(2), ..., P(x), and then add those together. The TI83/84 calculator has a built in function that does this calculation in one step. The function is binomcdf (n, p, x).
To calculate P(X 3) given n = 4, p = 0.41, and q = 0.59, press 2nd VARS [DISTR], ARROW DOWN to select A:binomcdf(, and then press ENTER.



After binomcdf(, type 4,.41,3), and then press ENTER. See the results below.

To 4 decimal places, the P (X 3) = 0.9717.
To find use the fact that = 1  P (X x  1).
Thus to find P (X 3) given n = 4, p = 0.41, and q = 0.59, compute 1  P(X 2) using binomcdf(4,.41,2) as is done directly above.