ProbabilityHardBloom L1
Question
'A' writes a letter to his friend 'B' and does not receive a reply. It is known that one out of ' $n$ ' letters does not reach its destination. The probability that ' $B$ ' didn't receive the letters is (It is certain that ' B ' would have replied, if he had received the letter)
Options
A.$\frac{1}{2}$
B.$\frac{1}{2n - 1}$
C.$\frac{2n - 1}{n^{2}}$
D.$\frac{n}{2n - 1}$
Solution
Sol. [Key Concept: 'A' writes to 'B', no reply: conditional probability of the letter being lost.]
$$P = \frac{\frac{1}{n} \times 1}{\frac{1}{n} \times 1 + \frac{n - 1}{n} \times \frac{1}{n}} = \frac{n}{2n - 1}$$
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