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Statistics Examples

P (A) = 0.006

$P (A) = 0.006$ ,

P (B) = 0.2

$P (B) = 0.2$ ,

P (B g i v e n A) = 0.3

$P (B g i v e n A) = 0.3$

Step 1

Using the Bayes' rule,

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

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

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) = 0.006

$P (A) = 0.006$ ,

P (B) = 0.2

$P (B) = 0.2$ , and

P (B | A) = 0.3

$P (B | A) = 0.3$ in Bayes' rule.

P (A | B) = \frac{(0.3) \cdot (0.006)}{0.2}

$P (A | B) = \frac{(0.3) \cdot (0.006)}{0.2}$

Step 3

Simplify

P (A | B) = \frac{(0.3) \cdot (0.006)}{0.2}

$P (A | B) = \frac{(0.3) \cdot (0.006)}{0.2}$ .

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Step 3.1

Multiply

0.3

$0.3$ by

0.006

$0.006$ .

P (A | B) = \frac{0.0018}{0.2}

$P (A | B) = \frac{0.0018}{0.2}$

Step 3.2

Divide

0.0018

$0.0018$ by

0.2

$0.2$ .

P (A | B) = 0.009

$P (A | B) = 0.009$

P (A | B) = 0.009

$P (A | B) = 0.009$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$