## Question

A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CACUTTA is

### Solution

4/11

Let *E*_{1} denote the event that the letter came from TATANAGAR and *E*_{2}the event that the letter came from CALCUTTA. Let A denote the event that the two consecutive alphabets visible on the envelope are TA. We have *P*(*E*_{1}) = 1/2, *P*(*E*_{2}) = 1/2,

Therefore, by Bayes’ theorem we have

#### SIMILAR QUESTIONS

Each of two persons *A* and *B* toss three fair coins. The probability that both get the same number of heads is

The probability that a student is not a swimmer is 1/5. The probability that out of 5 students exactly 4 is swimmer is

Six distinct numbers are selected from first 150 natural numbers. The probability all the six numbers are divisible both by 3 and 5 is

There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white is

A natural number *x* is chosen at random from the first one hundred natural numbers. The probability that is

An experiment has 10 equally likely outcomes. Let *A* and *B* two non – empty events of the experiment. If a consists of 4 outcomes, the number of outcomes that *B* must have so that *A* and *B* are independent, is

If *A*, *B* and *C* are the events such that *P*(*B*) = 3/4, *P*(*A* ∩ *B* ∩ *C’*) = 1/3*P*(*A’* ∩ *B* ∩ *C’*) = 1/3, then *P* (*B* ∩ *C*) is equal to

A fair coin is tossed n times. If the probability that head occurs 6 times is equal to the probability that occurs 8 times, then value of *n* is

A person writes 4 letters and addresses on 4 envelopes. If the letters are placed in the envelopes at random, the probability that not all letters are placed in correct envelopes is

A group of 6 boys and 6 girls is randomly divided into two equal groups. The probability that each group contains 3 boys and 3 girls is