Question

A letter is known to have come either from 'TATA NAGAR' or from 'CALCUTTA'. On the envelope, just two consecutive letters TA are visible. what is the probability that the letter came from 'TATA NAGAR' ?

Answer 1

The probability that the letter came from 'TATA NAGAR' given that the two consecutive letters TA are visible, we need to consider the total number of possibilities for the letter and the number of possibilities where the letter came from 'TATA NAGAR'. The probability is given by the number of ways two consecutive letters TA can appear from 'TATA NAGAR' divided by the total number of ways two consecutive letters TA can appear.

Step-by-step explanation:

To find the probability that the letter came from 'TATA NAGAR', we need to consider the total number of possibilities for the letter and the number of possibilities where the two consecutive letters TA are visible and the letter came from 'TATA NAGAR'.

Let's denote the event that the letter came from 'TATA NAGAR' as A and the event that the two consecutive letters TA are visible as B.

The probability that the letter came from 'TATA NAGAR' when the two consecutive letters TA are visible is given by:

P(A|B) = P(A ∩ B) / P(B)

Now, the probability that the two consecutive letters TA are visible is the same regardless of whether the letter came from 'TATA NAGAR' or 'CALCUTTA'. So, P(B) = P(Two consecutive letters TA are visible) = (Number of ways two consecutive letters TA can appear) / (Total number of possibilities for the letter)

Now, since the letter can only come from either 'TATA NAGAR' or 'CALCUTTA', the total number of possibilities for the letter is 2.

So, P(B) = (Number of ways two consecutive letters TA can appear) / 2

Therefore, the probability that the letter came from 'TATA NAGAR' when the two consecutive letters TA are visible is:

P(A|B) = P(A ∩ B) / P(B) = (Number of ways two consecutive letters TA can appear from 'TATA NAGAR') / (Number of ways two consecutive letters TA can appear)