Negative binomial distribution calculator
You can see a sample solution below. Enter your data to get the solution for your question
$$ \displaylines{---} $$
$$ \displaylines{N = 6
\\ \\
p = 0.5
\\ \\
q = p-1 = 0.5
\\ \\
r= 3
\\ \\
Formula\;for\;negative\;binomial\;distribution=
\, _{r-1}^{N-1}\textrm{C}(p)^{r}(q)^{N-r}
\\ \\
\mathbf{\color{Green}{For\;finding\;}}
\mathbf{\color{Green}{P(N>6)}}
\mathbf{\color{Green}{\;we\;have\;to\;find\;}}
\mathbf{\color{Green}{P(N<=6)}}
\mathbf{\color{Green}{\;first}}
\\ \\
P(N<=6) = \:\sum_{N=3}^{6}{_{3-1}^{N-1}\textrm{C}(0.5)^{3}(0.5)^{N- 3 } }
\\ \\ \Rightarrow
{_{3}^{3}\textrm{C}(0.5)^{3}(0.5)^{0}}
+
{_{3}^{4}\textrm{C}(0.5)^{3}(0.5)^{1}}
+
{_{3}^{5}\textrm{C}(0.5)^{3}(0.5)^{2}}
+
{_{3}^{6}\textrm{C}(0.5)^{3}(0.5)^{3}}
\\ \\ =
0.125
+
0.1875
+
0.1875
+
0.15625
\\ \\ =
0.65625
\\ \\
\mathbf{\color{Green}{P(N>6)\;=\;}}
\mathbf{\color{Green}{1\;-\;P(N<=6)}}
\\ \\ \Rightarrow
1-0.656250
\\ \\ \Rightarrow
\mathbf{\color{Red}{0.34375}}
} $$