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

Let events E1, E2 be the following:

E1 be the event that letter is from TATA NAGAR and E2 be the event that letter is from CALCUTTA


Let E be the event that on the letter, two consecutive letters TA are visible.


Since, the letter has come either from CALCUTTA or TATA NAGAR



When two consecutive letters are visible in the case of TATA NAGAR, we have following set of possible consecutive letters


{TA, AT, TA, AN, NA, AG, GA, AR}


In the case of CALCUTTA, we have following set of possible consecutive letters


{CA, AL, LC, CU, UT, TT, TA}


So, P(E|E1) is the probability that two consecutive letters are visible when letter came from TATA NAGAR


P(E|E2) is the probability that two consecutive letters are visible when letter came from CALCUTTA



We have to find the probability that the letter came from TATA NAGAR.


We use Bayes’ theorem to find the probability of occurrence of an event A when event B has already occurred.


∴


P(E|E1) is the probability that the letter came from TATA NAGAR






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