ProbabilityHardBloom L3
Question
India plays 2, 3 and 5 matches against Pakistan, Sri Lanka and Australia respectively. Probability that India win a match against Pakistan, Sri Lanka and Australia is 0.6, 0.5 and 0.4 respectively. If India win a match, then the probability that it was against Pakistan is
Options
A.$\frac{12}{47}$
B.$\frac{13}{47}$
C.$\frac{14}{47}$
D.$\frac{15}{47}$
Solution
Sol. [Key Concept: India vs Pak/SL/Aus — Bayes: $P(Pakmidwin)$.]
$$P = \frac{\frac{2}{10} \times 0.6}{\frac{2}{10} \times 0.6 + \frac{3}{10} \times 0.5 + \frac{5}{10} \times 0.4} = \frac{12}{47}$$
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