Question

A letter is known to have come either from $LONDON$ or $CLIFTON$; on the postmark only the two consecutive letters ON are eligible.

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

The correct option is B

$\frac{12}{17}$

Finding the probability that the letter came from the word LONDON:

Let $X$be the event that selects a pair of letters from LONDON,

Let $Y$ be the event that selects a pair of letters from CLIFTON.

Let $E$ be the event of selecting a pair of letters ON.

Hence,

$\begin{array}{rcl}P(X\cap E)& =& \frac{2}{5},\\ P(Y\cap E)& =& \frac{1}{6}\end{array}$

Therefore, the required probability $$\begin{gathered} =\frac{{\displaystyle \frac{2}{5}}}{\left[{\displaystyle \frac{2}{5}}+{\displaystyle \frac{1}{6}}\right]} \\ =\frac{\mathbf{12}}{\mathbf{17}} \end{gathered}$$$;\frac{\mathbf{P}\mathbf{(}\mathbf{X}\mathbf{\cap }\mathbf{E}\mathbf{)}\mathbf{}}{\mathbf{\left[}\mathbf{P}\mathbf{\right(}\mathbf{X}\mathbf{\cap }\mathbf{E}\mathbf{)}\mathbf{}\mathbf{+}\mathbf{P}\mathbf{(}\mathbf{Y}\mathbf{\cap }\mathbf{E}\mathbf{)}\mathbf{}\mathbf{}}$

Hence, the correct option is (B).