Calculer des probabilités dans le cadre d'une loi binomiale Exercice

p\left( X=4 \right)=\begin{pmatrix} 20 \cr\cr 4 \end{pmatrix}\left( \dfrac{1}{5}\right)^4\left( \dfrac{4}{5}\right)^{16}

p\left( X=4 \right)=\begin{pmatrix} 20 \cr\cr 4 \end{pmatrix}\left( \dfrac{1}{5}\right)^\text{16}\left( \dfrac{4}{5}\right)^{4}

p\left( X=4 \right)=\begin{pmatrix} 16 \cr\cr 4 \end{pmatrix}\left( \dfrac{1}{5}\right)^4\left( \dfrac{4}{5}\right)^{16}

p\left( X=4 \right)=\begin{pmatrix} 20 \cr\cr 4 \end{pmatrix}\left( \dfrac{1}{5}\right)^4\left( \dfrac{4}{5}\right)^{4}

p\left( X\geqslant18 \right)=\left( \dfrac{1}{5}\right)^\text{18}\left( 190\left( \dfrac{4}{5} \right)^2+20\times\dfrac{4}{25}+\dfrac{1}{25} \right)

p\left( X\geqslant18 \right)=\left( \dfrac{1}{5}\right)^\text{2}\left( 190\left( \dfrac{4}{5} \right)^2+20\times\dfrac{4}{25}+\dfrac{1}{25} \right)

p\left( X\geqslant18 \right)=\left( \dfrac{1}{5}\right)^\text{20}\left( 190\left( \dfrac{4}{5} \right)^2+20\times\dfrac{4}{25}+\dfrac{1}{25} \right)

p\left( X\geqslant18 \right)=\left( \dfrac{1}{5}\right)^\text{18}\left( 190\left( \dfrac{4}{5} \right)^{20}+20\times\dfrac{4}{25}+\dfrac{1}{25} \right)

p\left( X\geqslant1 \right)=1-\left( \dfrac{4}{5}\right)^{20}

p\left( X\geqslant1 \right)=\dfrac{1}{5}

p\left( X\geqslant1 \right)=\left( \dfrac{4}{5}\right)^{20}-1

p\left( X\geqslant1 \right)=1