A letter is known to have come either from 'TATA NAGAR or from 'CALCUTTA'. On the envelope, just two consecutive letter came from 'TATA NAGAR'?

Explanation

Also, let `E_(3)` be the event that on the letter , two consecutive letter TA are visible,
`thereforeP(E_(1))=1/2andP(E_(2))=1/2`
and `P(E_(3)//E_(1))=2/8and P(E_(3)//E_(2))=1/7`
[since, if letter is from TATA NAGAR, we see the events of teo consecutivbes letters visible are {TA, AT, TA, AN,NA, AG, GA, AR}. So, `P(E_(3)//E_(1))=2/8` and if letter is from CALCUTTA.
we see that the events of two consecutive letters to visible are {CA, AL, LC, CU, UT, TT, TA}
So, `P(E_(3)//E_(2))=1/7]`
`therefore P(E_(1)//E_(3))=(P(E_(1))cdotP(E_(3)//E_(1)))/(P(E_(1)cdotP(E_(3)//E_(1))+P(E_(2))cdotP(E_(3)//E_(2)))`
`=(1/2cdot2/8)/(1/2cdot2/8+1/2cdot1/7)=(1/8)/(1/8+1/14)=(1//8)/(22/(8xx14))=(1/8)/(11/56)=7/11`