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# Negative binomial distribution calculator

Total number of trials(N) : Exact N Less than or equal to N Greater than N

## You can see a sample solution below. Enter your data to get the solution for your question

$$\displaylines{---}$$
$$\displaylines{N = 6 \\ \\ p = 0.5 \\ \\ q = p-1 = 0.5 \\ \\ r= 3 \\ \\ Formula\;for\;negative\;binomial\;distribution= \, _{r-1}^{N-1}\textrm{C}(p)^{r}(q)^{N-r} \\ \\ \mathbf{\color{Green}{For\;finding\;}} \mathbf{\color{Green}{P(N>6)}} \mathbf{\color{Green}{\;we\;have\;to\;find\;}} \mathbf{\color{Green}{P(N<=6)}} \mathbf{\color{Green}{\;first}} \\ \\ P(N<=6) = \:\sum_{N=3}^{6}{_{3-1}^{N-1}\textrm{C}(0.5)^{3}(0.5)^{N- 3 } } \\ \\ \Rightarrow {_{3}^{3}\textrm{C}(0.5)^{3}(0.5)^{0}} + {_{3}^{4}\textrm{C}(0.5)^{3}(0.5)^{1}} + {_{3}^{5}\textrm{C}(0.5)^{3}(0.5)^{2}} + {_{3}^{6}\textrm{C}(0.5)^{3}(0.5)^{3}} \\ \\ = 0.125 + 0.1875 + 0.1875 + 0.15625 \\ \\ = 0.65625 \\ \\ \mathbf{\color{Green}{P(N>6)\;=\;}} \mathbf{\color{Green}{1\;-\;P(N<=6)}} \\ \\ \Rightarrow 1-0.656250 \\ \\ \Rightarrow \mathbf{\color{Red}{0.34375}} }$$