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Question: A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecut...

A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters TA are visible . The probability that the letter has come from CALCUTTA is

A

4/11

B

1/3

C

5/12

D

None of these

Answer

4/11

Explanation

Solution

Let E1 denote the event that the letter came from TATANAGAR and E2 the event that the letter came from CALCUTTA. Let A denote the event that the two consecutive alphabets visible on the envelope are TA. We have P(E1)

= 1/2, P(E2) = 1/2, P(A / E1) = 2/8, P (A / E2) = 1/7.

Therefore, by Bayes' theorem we have P(E2 / A)

= = 411\frac { 4 } { 11 }