ProbabilityMedium
Question
A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:
Options
A.$\frac{7}{10}$
B.$\frac{10}{17}$
C.$\frac{12}{19}$
D.$\frac{7}{19}$
Solution
Sol. [Key Concept: Bayes' theorem: weight each origin by $P(``AN''\ visiblemidcity) = \frac{\#\ consecutive\ AN}{letters - 1}$.]
$${P(I):\frac{1}{2}P(A/I) \rightarrow \frac{1}{5} }{P(II):\frac{1}{2}P(A/II) \rightarrow \frac{2}{7} }$$∴ Reqd. Prob $= \frac{\frac{1}{2} \times \frac{2}{7}}{\frac{1}{2} \times \frac{1}{5} + \frac{1}{2} \times \frac{2}{7}} = \frac{\frac{2}{7} \times 5}{\frac{17}{7}} = \frac{10}{17}$
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