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

Question

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

Philoid · Accepted Answer

Let us assume U₁, U₂ and A be the events as follows:

U₁ = Letter comes from LONDON

U₂ = Letter comes from CLIFTON

A = Event of getting two visible consecutive letters are ON

We know that letter comes from each place is most likely to occur. So, probability of getting letter will be same from each place.

⇒

Now,

⇒ P(A|U₁) = P(visible two letters ON from london )

⇒

⇒ P(A|U₂) = P(visible two letters ON from CLIFTON)

⇒

Now we find

P(U₁|A) = P(The envelope comes from LONDON)

P(U₂|A) = P(The envelope comes from CLIFTON)

Using Baye’s theorem:

⇒

The required probabilities are .

A letter is known to have come either from LONDON or CLIFTON. On the envelope just two consecutive letters are visible. What is the probability that the letter has come fromi. LONDONii. CLIFTON

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

ii. CLIFTON