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P (A) = 0.08

$P (A) = 0.08$ ,

P (B) = 0.78

$P (B) = 0.78$ ,

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

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

Step 1

Using the Bayes' rule,

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

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

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) = 0.08

$P (A) = 0.08$ ,

P (B) = 0.78

$P (B) = 0.78$ , and

P (B | A) = 0.1

$P (B | A) = 0.1$ in Bayes' rule.

P (A | B) = \frac{(0.1) \cdot (0.08)}{0.78}

$P (A | B) = \frac{(0.1) \cdot (0.08)}{0.78}$

Step 3

Simplify

P (A | B) = \frac{(0.1) \cdot (0.08)}{0.78}

$P (A | B) = \frac{(0.1) \cdot (0.08)}{0.78}$ .

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Step 3.1

Multiply

0.1

$0.1$ by

0.08

$0.08$ .

P (A | B) = \frac{0.008}{0.78}

$P (A | B) = \frac{0.008}{0.78}$

Step 3.2

Divide

0.008

$0.008$ by

0.78

$0.78$ .

P (A | B) = 0.0\overline{102564}

$P (A | B) = 0.0\overline{102564}$

P (A | B) = 0.0\overline{102564}

$P (A | B) = 0.0\overline{102564}$

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

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