`P(n,S,p) = B_C( "n" / "S" ) * "p" ^ "S" * q^( "n" - "S" )`

Enter a value for all fields

The Probability of an Event calculator computes the probability of an event A ,P(A), if there are a certain number of favorable outcomes possible (F) out of all of the evenly possible outcomes (T).

INSTRUCTIONS: Enter the following:

• (F)  Enter the number of possibly favorable outcomes.
• (T)  Enter the total number of equally possible outcomes.

Probability of Event A: The calculator returns the probability (P) as a real.  However, this can be automatically converted to a percentage via the pull-down menu.  This calculator uses the Binomial Coefficient (CLICK HERE).  This calculator is also a prominent feature with other statistical functions in the College Level Statistics Calculator (Stat Calc).

Binomial Distribution

Binomial Distribution is useful when there are two possible outcomes on any trial and when the events of one trial do not effect results of any subsequent trial.  In this case, one is simply summing the probabilities of a series of trials.  This calculator takes advantage of method that employs the binomial coefficient in the following formula:

Probability of S successes in n trials ( P (n/S) ) is equal to:   

                P(n/S) = B_C * p^S * q^n-S

where:

• p is the probability of success on any trial.
• q is the probability of failure, and therefore equal to 1 - p
• B_C is the binomial coefficient derived from Pascal's Triangle. 

References

•  Naiman, Arnold, Robert Rosenfeld, and Gene Zirkel. "Common Statistical Measures."Understanding Statistics. 2nd ed. N.p.: n.p., 1977. 62. Print.