Question

A letter is known to have come eithe from London or Clifton; on the post only the consecutive letters ON are legible; what is the chance that it came from London?

• A. $\frac{12}{17}$
• B. $\frac{5}{17}$
• C. $\frac{5}{12}$
• D. $\frac{7}{12}$

Answer 1

The correct option is A $\frac{12}{17}$

If letter came from Clifton there are $6$ pairs of consecutive letters i.e., $cl,li,if,ft,to$, $ON$ in which $ON$ appears only once.
$\therefore$ the chance that this was the legible couple on the Clifton hypothesis $=\frac{1}{6}$
pairs of consecutive letters in the word London are $lo,on,nd,do$, $ON$ in which $ON$ occurs twice.
$\therefore$ the chance that this was the legible couple on the London hypothesis$=2/5.$
$\therefore$ The a posteriori chances that the letter was from Clifton or London are $\frac{1/6}{\frac{1}{6}+\frac{2}{5}}$ and $\frac{2/5}{\frac{1}{6}+\frac{2}{5}}$ respectively.
Thus the reqd.chance $=\frac{12}{17}.$