Question

A letter is known to have come either from LONDON or CLIFTON; on the postmark only the two consecutive letters ON are legible. The probability that it came from LONDON is

• A. $\frac { 5 } { 17 }$
• B. $\frac { 12 } { 17 }$
• C. $\frac { 17 } { 30 }$
• D. $\frac { 3 } { 5 }$

Answer 1

Answer: (B)

$\frac { 12 } { 17 }$

Answer 2

We define the following events :

Selecting a pair of consecutive letter from the word LONDON.

$A _ { 2 } :$ Selecting a pair of consecutive letters from the word CLIFTON.

E : Selecting a pair of letters ‘ON’.

Then $P \left( A _ { 1 } \cap E \right) = \frac { 2 } { 5 }$ as there are 5 pairs of consecutive letters out of which 2 are ON.

$P \left( A _ { 2 } \cap E \right) = \frac { 1 } { 6 }$ as there are 6 pairs of consecutive letters of which one is ON.

∴ The required probability is

$P \left( \frac { A _ { 1 } } { E } \right)$ $= \frac { P \left( A _ { 1 } \cap E \right) } { P \left( A _ { 1 } \cap E \right) + P \left( A _ { 2 } \cap E \right) } = \frac { \frac { 2 } { 5 } } { \frac { 2 } { 5 } + \frac { 1 } { 6 } } = \frac { 12 } { 17 }$.