# Negative Binomial Summary for n = 6, r = 3 & P = 0.14 Negative binomial probability function solved example work with steps & calculation summary to estimate probability of total number of failures P(r) for number of failures X = 3, success probability for each trial P = 0.14 from the total number of events n = 6.

Calculation Summary
Number of Possibility (n)6
Number of Failures (r)3
Trial Probability (P)0.14
Negative Binomial distribution0.0003

## Work with Steps for n = 6, r = 3 & P = 0.14

The below is the complete work with step by step calculation for n = 6 , r = 3, p = 0.14 to estimate the probability of total number of failures in statistical experiments.
Workout :
step 1 Address the formula input parameters and values
Number of Possibility (n) = 6
Number of Failures (r) = 3
Probability (P) = 0.14
P(x)= r+n-1Cr Pn qr

step 2 Find value for 8 C 3 or 8 CHOOSE 3
8C3 = 8!/3!(8-3)!
= 8!/3! x 5!
= 40320/6 x 120
8C3 = 56

step 3 Find q value from P
q = 1 - P
q = 1 - 0.14
q = 0.86

step 4 Apply 8C3, P & q values in Negative binomial distribution formula
P(x) = 56 x 0.146 x 0.863

step 5 solve the expression
= 56 x 0.146 x 0.863
= 56 x 0 x 0.636056
P(x) = 0.0003

Thus 0.0003 is the probability of total number of 3 failures from 6 events with 0.14 failure probability for each trial 