IntroStatsCalc

Binomial Probability

P(X = x), at most, at least, and between, with binompdf and binomcdf commands.

Inputs

Probability that X is

Results update as you type.

Results

P(X = 3) = 0.2668

The probability of exactly 3 successes in 10 trials is 0.2668, or about 26.68%.

Binomial (n = 10, p = 0.3) probability bars for x = 0 to 10. The highlighted bars are the outcomes exactly 3; together they have probability 0.2668.012345678910x

Results

P(X = 3)0.2668
Mean μ3
Standard deviation σ1.4491

On the TI-84

2nd VARS (DISTR) → A:binompdf( for “exactly”, or B:binomcdf( for “at most” (binomcdf adds up P(0) through P(x)).

binompdf(10, 0.3, 3)

Show steps
  1. Check the conditions. A fixed number of trials (n = 10), two outcomes, the same probability of success each trial (p = 0.3), and independent trials.
  2. Formula. P(X = x) = nCx · px · (1 − p)n − x
  3. Substitute. P(X = 3) = 10C3 · 0.33 · 0.77 = 120 · 0.027 · 0.082354 = 0.2668
  4. Mean and SD. μ = np = 10(0.3) = 3; σ = √(np(1 − p)) = √2.1 = 1.4491.

About this calculator

When is it binomial?

A binomial setting has a fixed number of trials n, each trial is a success or a failure, the probability of success p is the same every time, and the trials are independent. X counts the successes.

Translating the words

The mean of a binomial distribution is μ = np and the standard deviation is σ = √(np(1 − p)).

More probability calculators: Counting (nPr, nCr) · Discrete Distribution · Poisson · Geometric