Solutions - 5080-06

(a)

$X\sim \text{Bin}(10,0.3)$

$$\begin{array}{c}P[X<2]=P[X=0]+P[X=1]\\ \\ \gg \gg \left(\genfrac{}{}{0px}{}{10}{0}\right){(0.3)}^0{(0.7)}^{10}+\left(\genfrac{}{}{0px}{}{10}{1}\right){(0.3)}^1{(0.7)}^9\\ \\ \gg \gg {0.7}^{10}+10\cdot 0.3\cdot {(0.7)}^9\gg \gg 0.1493\end{array}$$

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(b)

$Y\sim \text{Geo}(0.3)$

$$\begin{array}{c}P[Y\ge 3]=1-P[Y=1]-P[Y=2]\\ \\ \gg \gg 1-0.3\cdot {(0.7)}^0-0.3\cdot {(0.7)}^1\gg \gg 0.49\end{array}$$