Probability Question 177
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
Options:
A) $ \frac{5}{17} $
B) $ \frac{12}{17} $
C) $ \frac{17}{30} $
D) $ \frac{3}{5} $
Show Answer
Answer:
Correct Answer: B
Solution:
We define the following events :
$ A_1: $ 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(A_1\cap E)=\frac{2}{5}; $ as there are 5 pairs of consecutive letters out of which 2 are ON. $ P(A_2\cap E)=\frac{1}{6}; $
as there are 6 pairs of consecutive letters of which one is ON.
The required probability is $ P( \frac{A_1}{E} ) $
$ =\frac{P(A_1\cap E)}{P(A_1\cap E)+P(A_2\cap E)}=\frac{\frac{2}{5}}{\frac{2}{5}+\frac{1}{6}}=\frac{12}{17}. $
BETA
