91影视

$W_i$- event that the $i$-th component works, $i鈭�\{1,2,鈥�n\}$.

$P\left(W_i\right)=P_i,i鈭�\{1,2,鈥�n\}$.

$P\left(W_1鈭�1-\text{out}-\text{of}-2\right)=\frac{P\left(1-\text{out}-\text{of}-2鈭�W_1\right)P\left(W_1\right)}{P(1-out-of-2)}$

Because of what$1-$out $-$of $-2$means $P\left(1-\right.$out $-$of $\left.-2鈭�W_1\right)=1$, and $P\left(W_1\right)=P=\frac{1}{2}$, and boxed formula in box $1$yields:

${\left.P(1-\text{out}-\text{of}-2)=\underset{1鈮�l鈮�2}{鈭�}\left(\begin{array}{l}2\\ l\end{array}\right){\left(\frac{1}{2}\right)}^l{\left(1-\frac{1}{2}\right)}^{2-l}=\left(\begin{array}{l}2\\ 1\end{array}\right){\left(\frac{1}{2}\right)}^2+{\left(\begin{array}{l}2\\ 2\end{array}\right)}^{\frac{1}{2}}\right)}^2=\frac{3}{4}$

Now these probabilities can be substituted into formula above:

$P\left(W_1鈭�1-\text{out}-\text{of}-2\right)=\frac{1路\frac{1}{2}}{\frac{3}{4}}=\frac{2}{3}$.

The probabilities$P\left(W_1鈭�1-\text{out}-\text{of}-2\right)=\frac{2}{3}$.

$W_i$- event that the $i$-th component works, $i鈭�\{1,2,鈥�n\}$.

$P\left(W_i\right)=P_i,i鈭�\{1,2,鈥�n\}$.

$P\left(W_1鈭�2-\text{out}-\text{of}-3\right)=\frac{P\left(2-\text{out}-\text{of}-3鈭�W_1\right)P\left(W_1\right)}{P(2-\text{out}-\text{of}-3)}$

If $W_1$occurred, $2$- out $-$of $-3$means that in $W_2,W_3-2$components, 1 more has to be working, and since these are independent, identically distributed:

$P\left(2-out-of-3鈭�W_1\right)=P(1-out-of-2)\stackrel{a)}{=}\frac{3}{4}$

And for the denominator use boxed formula in box $1$:

$P(2-\text{out}-\text{of}-3)=\underset{2鈮�l鈮�3}{鈭�}\left(\begin{array}{l}3\\ l\end{array}\right){\left(\frac{1}{2}\right)}^l{\left(1-\frac{1}{2}\right)}^{3-l}=\left(\begin{array}{l}3\\ 2\end{array}\right){\left(\frac{1}{2}\right)}^3+\left(\begin{array}{l}3\\ 3\end{array}\right){\left(\frac{1}{2}\right)}^3=\frac{4}{8}=\frac{1}{2}$

This is all that is needed to calculate the probability by the stated formula:

$P\left(W_1鈭�2-\text{out}-\text{of}-3\right)=\frac{\frac{3}{4}路\frac{1}{2}}{\frac{1}{2}}=\frac{3}{4}$

The probabilities$P\left(W_1鈭�2-\text{out}-\text{of}-3\right)=\frac{3}{4}$.