Mr. X travels from Delhi to Muscat with change of airplanes in Chennai, Dubai and Sharjah respectively. He has one piece of luggage. At each stop the luggage is transferred from one airplane to another. At the airport in Delhi there is a probability of $\frac{1}{20}$ that luggage is not placed in right plane. This probability is $\frac{1}{10}$ at airport in Chennai, $\frac{1}{5}$ at airport in Dubai and $\frac{1}{10}$ at airport in Sharjah

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The probability that Mr. X luggage does not reach Sharjah with him is 0.316

If Mr. X luggage does not reach muscat with him, then the probability that it was lost at airport of Dubai is $\frac{715}{1922}$

The probability that Mr. X luggage does not reach Sharjah with him 0.512

If Mr. X luggage does not reach muscat with him, then the probability that it was lost at airport of Dubai is $\frac{855}{1922}$

answer is A, B.

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Detailed Solution

Delhi $\to$ Chennai $\to$ Dubai $\to$ Sharjah $\to$ Muscat
P (Luggage does not reach Sharjah)
$1 - (1 - \frac{1}{20}) (1 - \frac{1}{10}) (1 - \frac{1}{5}) = 1 - \frac{19}{20} . \frac{9}{10} . \frac{4}{5} = 1 - \frac{684}{1000} = \frac{316}{1000} = 0.316$

$P (\frac{luggage was lost at Dubai}{luggage does not reach Muscat})$

$\frac{(1 - \frac{1}{20}) (1 - \frac{1}{10}) \frac{1}{5}}{1 - (1 - \frac{1}{20}) (1 - \frac{1}{10}) (1 - \frac{1}{5}) (1 - \frac{1}{10})} = \frac{855}{1922}$