Question

A letter is known to come either from TATANAGAR or CALCUTTA. On the envelope, Just to consecutive letters TA are visible. What is the probability that the letter came from TATANAGAR ?

(A) 4/11
(B) 1/3
(C) 5/12
(D) 1/7

Answer 1

The probability that the letter came from TATANAGAR given the sequence 'TA' is visible is 2/3, as TATANAGAR contains two 'TA' sequences and CALCUTTA contains one. The answer is not among the given options.

Step-by-step explanation:

The probability that the letter came from TATANAGAR can be found using the principle of conditional probability. Since the only visible letters on the envelope are 'TA', we must consider how many times the sequence 'TA' appears in each of the two words. TATANAGAR has 'TA' appearing twice ('TA-TA-NAGAR'), while CALCUTTA has it appearing only once ('CALCU-TA').

Hence, if 'TA' is visible, there are three possible places it could have come from, two from TATANAGAR and one from CALCUTTA. We are assuming the likelihood is equal for all instances the letters 'TA' appear on any given envelope. The probability, then, that the envelope is from TATANAGAR is the number of instances in TATANAGAR divided by the total instances across both locations, which is:

Probability = Number of 'TA' in TATANAGAR / Total Number of 'TA'

Probability = 2/3

Therefore, the correct answer is not listed among the given options.