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GATE PI 2014 Official Paper

Option 4 : 27/41

**Concept:**

**Bayes' Theorem:** It is a mathematical formula for determining conditional probability.

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

**Calculation:**

**Given:**

P(raining) = \(7 \over 10\) ⇒ P(not-raining) = \(3 \over 10\); P(loss/rain) = \(8 \over 10\) ⇒ P(no-loss/rain) = \(2 \over 10\);

P(loss/no-rain) = \(1 \over 10\) ⇒ P(no-loss/no-rain) = \(9 \over 10\);

**Probability of no-rain for no loss on a given day is calculated as**

P(no-rain / no-loss) = \(\frac {P(no-loss/no-rain)\ \times \ P(not-raining)}{P(raining)\ \times\ P(no-loss/raining) \ +\ P(not-rainnig)\ \times \ P(no-loss/no ~raining) }\)

P(no-rain / no-loss) = \(\frac {\frac {9}{10}\ \times \ \frac {3}{10}}{\frac {7}{10}\ \times\ \frac {2}{10} \ +\ \ \frac {9}{10}\ \times \ \frac {3}{10} }\)

**P(no-rain / no-loss) = \(\frac {27}{41}\)**