Problem 77P

Consider an unending sequence of independent trials, where each trial is equally likely to result in any of the outcomes 1, 2, or 3. Given that outcome 3 is the last of the three outcomes to occur, find the conditional probability that

(a) the first trial results in outcome 1;

(b) the first two trials both result in outcome 1.

Solution:

Step 1 of 3:

It is given that each trial is equally likely to result any one of the outcomes 1,2,3 in a unending sequence of independent trials.

Also, it is given that 3 is last outcome to occur.

Using this we need to find the required conditional probabilities.