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.

Question

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

Answer 1

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

$\begin{array}{cc} L e f t & R i g h t & T o t a l \\ F e m a l e & 11 & 104 & 115 \\ M a l e & 24 & 92 & 116 \\ T o t a l & 35 & 196 & 231 \end{array}$

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

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.

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