حل تشریحی سوال شماره 223 ریاضی و آمار 3 انسانی

الف)

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$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{\left(\begin{array}{c}5\\ 2\end{array}\right)\times \left(\begin{array}{c}4\\ 1\end{array}\right)}{\left(\begin{array}{c}9\\ 3\end{array}\right)}=\frac{10\times 4}{84}=\frac{10}{21}$

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$P(B)=\frac{n(B)}{n(S)}=\frac{\left(\begin{array}{c}4\\ 2\end{array}\right)\times \left(\begin{array}{c}5\\ 1\end{array}\right)+\left(\begin{array}{c}4\\ 3\end{array}\right)}{\left(\begin{array}{c}9\\ 3\end{array}\right)}=\frac{6\times 5+4}{84}=\frac{34}{84}=\frac{17}{42}$

روش دوم:

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$P(B)=1-P(B^{\prime })=1-\frac{\left(\begin{array}{c}4\\ 2\end{array}\right)\times \left(\begin{array}{c}5\\ 2\end{array}\right)+\left(\begin{array}{c}5\\ 3\end{array}\right)}{\left(\begin{array}{c}9\\ 3\end{array}\right)}=1-\frac{4\times 10+10}{84}=1-\frac{50}{84}=\frac{34}{84}$