User:HJH3

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======== Project 94 ===================== $$ \begin{align} \int_0^1 P( m=7|r, n=10) \, f(r) \, dr & = \int_0^1 {10 \choose 7} \, r^7 \, (1-r)^3 \, 1 \, dr \\ & = {10 \choose 7} \left / {11 \choose 3,7,1} \right. = {10 \choose 7} \, \frac{1}{1320} \end{align} $$

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Project 95 ============ $$ \begin{align} \int_0^1 P( m=7|r, n=10) \, f(r) \, dr & = \int_0^1 {10 \choose 7} \, r^7 \, (1-r)^3 \, 1 \, dr \\ & = {10 \choose 7} \left / {11 \choose 3,7,1} \right. = {10 \choose 7} \, \frac{1}{1320} \end{align} $$

Project 94
$$ \begin{align} \int_0^1 P( m=7|r, n=10) \, f(r) \, dr & = \int_0^1 {10 \choose 7} \, r^7 \, (1-r)^3 \, 1 \, dr \\ & = {10 \choose 7} \left / {11 \choose 3,7,1} \right. = {10 \choose 7} \, \frac{1}{1320} \end{align} $$

Project 95
$$ \begin{align} \int_0^1 P( m=7|r, n=10) \, f(r) \, dr & = \int_0^1 {10 \choose 7} \, r^7 \, (1-r)^3 \, 1 \, dr \\ & = {10 \choose 7} \left / {11 \choose 3,7,1} \right. = {10 \choose 7} \, \frac{1}{1320} \end{align} $$