A letter is known to have come either from LONDON or CLIFTON. On the envelope just two consecutive letters ON are visible. What is the probability that the letter has come from (i) LONDON (ii) CLIFTON?

Options

A. `1//7`
B. `12//17`
C. `17//30`
D. `3//5`

Answer

B

Explanation

We define the following events:
`A_(1):` Selecting a pair of consecutive letters from the word LONDON
`A_(2):` Selecting a pair of consecutive letters from the word CLIFTON
E: Selecting a pair of letter 'ON'
Then, `P(A_(1)nnE)=2//5` as there are 5 pairs of consecutive letters out of which e are ON and `P(A_(2)nnE)=1//6` as there are 6 pairs of consective letters of which 1 is ON. Therefore, the required probability is
`P((A_(1))/(E))=(P(A_(1)nnE))/(P(A_(1)nnE)+P(A_(2)nnE))=(2/5)/(2/5+1/6)=12/17`