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Question

A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letter TA are visible. The probability that the letter has come from CALCUTTA is
  1. 411
  2. 13
  3. 512
  4. 17


Solution

The correct option is A 411
Let T be the event that the letter has arrived from TATANAGAR and C be the event that the letter has arrived from CALCUTTA
P(T)=12,P(C)=12

The probability that TA comes from TATANAGAR is, 
P(TA|T)=28
The probability that TA comes from CALCUTTA is,
P(TA|C)=17

Using Bayes theorem :
P(C|TA)=P(TA|C)P(C)P(TA|C)P(C)+P(TA|T)P(T)
                =1717+14=411
 

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