Question

A letter is known to have come either from london or clifton. On the postmark only the two consecutive letters on are visible. The probability that it came from london is

Answer 1

Answer:

Step-by-step explanation:

Let E1 --> Letters came from the word LONDON

and E2 --> Letters came from the word CLIFTON

Since the letters have to come from either of these two words

P(E1) = P(E2) = 1/2

Let A --> Two consecutive letters on the envelope are ON

If E1 occurs then the letters ON come from the word LONDON. In this word there are 6 letters in which ON occurs twice. Considering one of the ON's as one object/letter there are now 5 letters.

Therefore

P(A/E1) = 2/5

Now if E2 occurs, then the letters come form the word CLIFTON. In this there are 7 letters in which ON occurs once. Considering ON as one object/letter there are now 6 letters.

Therefore

P(A/E2) = 1/6

Baye's Theorem

(i) P(E1/A) = ( 1/2 * 2/5 ) / ( 1/2 * 2/5 + 1/2 * 1/6 )

---------> = 2/5 * 30/17

---------> = 12/17 ( ans )