Answer :

Let events E_{1}, E_{2} be the following:

E_{1} be the event that letter is from TATA NAGAR and E_{2} 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|E_{1}) is the probability that two consecutive letters are visible when letter came from TATA NAGAR

P(E|E_{2}) 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|E_{1}) is the probability that the letter came from TATA NAGAR

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