Geometric distribution is a probability model and statistical data that is used to find out the number of failures which occurs before single success

p = probability of success for a single trial q = probability of failure for a single trial ( = 1-p ) x = number of failures (= 0, 1, 2 ...) p+q = 1

A boy rolling a die. Calculate the probability of getting 3 on the 6th roll.

Let us first calculate p which is the probability of success for a single trial p = 1/6 = 0.166.

Now, find the value of q. q = probability of failure for a single trial ( = 1-p ) q = (1 - 1/6) q = 0.834 . (Note : p + q = 1)

Calculate the value of x. x denotes the number of failures before a success. x= 6-1 => x = 5.

Now, substitute the value of p, q and x in the formula,
**P(x) = q ^{x}p**
P(5) = (0.834