# Bayes' Theorem is given byP(A|B) = frac{P(B|A) cdot P(A)} {P(B)}.Use a two-way table to write an example of Bayes' Theorem.

Bayes' Theorem is given by $P\left(A|B\right)=\frac{P\left(B|A\right)\cdot P\left(A\right)}{P\left(B\right)}$. Use a two-way table to write an example of Bayes' Theorem.

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aprovard

Possible answer: The two-way tables from exercise 7 was:

$\begin{array}{cccc}& Left& Right& Total\\ Female& 11& 104& 115\\ Male& 24& 92& 116\\ Total& 35& 196& 231\end{array}$

Two events could then be male (A) and right handed (B). From the table, $P\left(A\right)=\frac{116}{31}$ and $P\left(B\right)=\frac{196}{231}$ since there are 116 males and 196 right handed people. Since there are 92 right handed males and 116 males, then $P\left(B\mid A\right)=\frac{92}{116}$ From the table, there are 196 right handed people and 92 of them are male so $P\left(A\mid B\right)=\frac{92}{196}=\frac{23}{49}.$ Using Bayes’ Theorem, $P\left(B\mid A\right)=\frac{P\left(B\mid A\right)\cdot P\left(A\right)}{P\left(B\right)}=\frac{\frac{92}{116}\cdot \frac{116}{231}}{\frac{196}{231}}$ which is equal to the previous answer you found.