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

p\left( X=4 \right)=\begin{pmatrix} 34 \cr\cr 4 \end{pmatrix}\left( \dfrac{1}{4}\right)^4\left( \dfrac{3}{4}\right)^{31}

p\left( X=4 \right)=\begin{pmatrix} 34 \cr\cr 4 \end{pmatrix}\left( \dfrac{1}{4}\right)^4\left( \dfrac{3}{4}\right)^{30}

p\left( X=4 \right)=\begin{pmatrix} 30 \cr\cr 4 \end{pmatrix}\left( \dfrac{1}{4}\right)^4\left( \dfrac{3}{4}\right)^{30}

p\left( X=4 \right)=\begin{pmatrix} 20 \cr\cr 4 \end{pmatrix}\left( \dfrac{1}{4}\right)^4\left( \dfrac{3}{4}\right)^{4}

p\left( X\geqslant32 \right)=\left( \dfrac{1}{4}\right)^\text{32}\left( 561\left( \dfrac{3}{4} \right)^2+34\times\dfrac{3}{16}+\dfrac{1}{16} \right)

p\left( X\geqslant32 \right)=\left( \dfrac{1}{4}\right)^\text{30}\left( 561\left( \dfrac{3}{4} \right)^2+34\times\dfrac{3}{16}+\dfrac{1}{16} \right)

p\left( X\geqslant32 \right)=\left( \dfrac{1}{4}\right)^\text{28}\left( 561\left( \dfrac{3}{4} \right)^2+34\times\dfrac{3}{16}+\dfrac{1}{16} \right)

p\left( X\geqslant 32\right)=\left( \dfrac{1}{4}\right)^\text{32}\left( 561\left( \dfrac{3}{4} \right)^2+34\times\dfrac{3}{4}+\dfrac{1}{4} \right)

p\left( X\geqslant1 \right)=1-\left( \dfrac{3}{4}\right)^{34}

p\left( X\geqslant1 \right)=\dfrac{1}{4}

p\left( X\geqslant1 \right)=\left( \dfrac{3}{4}\right)^{34}-1

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