Question

It is known that a letter comes from either 'tata nagar' or

'kolkata'. But only the two consecutive letters TA are visible

on post mark. Then the prob., that letter comes from tatanagar

is

• A. 2/5
• B. 1/5
• C. 3/5
• D. 4/5

Answer 1

Answer: (C)

3/5

Answer 2

A & B be the events of receiving letters from Tatanagar & Kolkata respectively.

P(1) = $\frac { 1 } { 2 }$; P(2) = $\frac { 1 } { 2 }$

Let E be event that TA is visible and remaining letters are

wiped of

P(E/A) = $\frac { 2 } { 8 } = \frac { 1 } { 4 }$

P(E/B) = $\frac { 1 } { 6 }$

P(A/E) = $\frac { \frac { 1 } { 2 } \times \frac { 1 } { 4 } } { \frac { 1 } { 2 } \times \frac { 1 } { 4 } + \frac { 1 } { 2 } \times \frac { 1 } { 6 } } = \frac { \frac { 1 } { 4 } } { \frac { 6 + 4 } { 6 \times 4 } } = \frac { 6 } { 10 } = \frac { 3 } { 5 }$