Sagot :
[tex] \bold{Note° \: that \: \sum_{i=1}^C P(i|t)=1}\\ \bold{thats \: is \: how \: the \: obtain \: in \: the \: simpication.}[/tex]
[tex] \bold{\begin{align}I_g(t) & \bold{= \sum_{i=1}^c p(i|t) (1 - p(i|t)) }\\& \bold{= \sum_{i=1}^c (p(i|t) - p(i|t)^2) }\\& \bold{= \sum_{i=1}^c p(i|t)- \sum_{i=1}^cp(i|t)^2}\\& \boxed{ \bold{=1- \sum_{i=1}^cp(i|t)^2}} \end{align}} \\ \bold{or} \\ \boxed{\bold{\sum_{i=1}^{c} p(i|t) = 1}}[/tex]