A letter is known to have either from "TATA NAGAR" or from "CALCUTTA". On the envelope, just two consecutive letters TA are visible. If the probability that the letter came from 'TATA NAGAR" is in the form p q , where p and q are co-prime positive integers, then find the value of (p+q) .

Step-by-step solution

Let A be the event that the letter is from TATANAGAR and B be the event that letter is from CALCUTTA. Also, let E be the event that on the letter, two consecutive letters TA are visible. P(A)= 1 2 ; P(B)= 1 2 And P(E / A)= 2 8 and P(E / B)= 1 7 [If the letter is TATANAGAR, we see that the events of two consecutive letters visible are TA, AT, TA, AN, NA, AG, GA, AR] Sô, P(E / A)= 2 8 and sāmé in cãsè of CALCUTTA, soo P(E / B)= 1 7 Therefore, P(A / E)= P(A) P(E / A) P(A) P(E / A)+P(B) P(E / B) = (1 / 2)(2 / 8) [(1 /