# 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 distribution | 0.0003 |

## 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-1}C_{r} P^{n} q^{r}

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 0.14^{6} x 0.86^{3}

step 5 solve the expression

= 56 x 0.14^{6} x 0.86^{3}

= 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