# Negative Binomial Summary for n = 15, r = 3 & P = 0.5

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 = 0.5 from the total number of events n = 15.

Calculation Summary | |
---|---|

Number of Possibility (n) | 15 |

Number of Failures (r) | 3 |

Trial Probability (P) | 0.5 |

Negative Binomial distribution | 0.0026 |

## Work with Steps for n = 15, r = 3 & P = 0.5

The below is the complete work with step by step calculation for n = 15 , r = 3, p = 0.5 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) = 15

Number of Failures (r) = 3

Probability (P) = 0.5

P(x)= ^{r+n-1}C_{r} P^{n} q^{r}

step 2 Find value for *17 C 3 or 17 CHOOSE 3*

17C3 = 17!/3!(17-3)!

= 17!/3! x 14!

= 355687428096000/6 x 87178291200

17C3 = 680

step 3 Find q value from P

q = 1 - P

q = 1 - 0.5

q = 0.5

step 4 Apply 17C3, P & q values in Negative binomial distribution formula

P(x) = 680 x 0.5^{15} x 0.5^{3}

step 5 solve the expression

= 680 x 0.5^{15} x 0.5^{3}

= 680 x 0 x 0.125

P(x) = 0.0026

Thus 0.0026 is the probability of total number of 3 failures from 15 events with 0.5 failure probability for each trial