Statistics Examples

$P (A) = 0.1$ , $P (B) = 0.012$ , $P (B g i v e n A) = 0.1$

Step 1

Using the Bayes' rule, $P (A | B) = \frac{P (B | A) P (A)}{P (B)}$ .

$P (A | B) = \frac{P (B | A) P (A)}{P (B)}$

Step 2

Substitute the given values $P (A) = 0.1$ , $P (B) = 0.012$ , and $P (B | A) = 0.1$ in Bayes' rule.

$P (A | B) = \frac{(0.1) \cdot (0.1)}{0.012}$

Step 3

Simplify $P (A | B) = \frac{(0.1) \cdot (0.1)}{0.012}$ .

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Step 3.1

Multiply $0.1$ by $0.1$ .

$P (A | B) = \frac{0.01}{0.012}$

Step 3.2

Divide $0.01$ by $0.012$ .

$P (A | B) = 0.8\overline{3}$

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