# Question: Consider an unending sequence of independent trials where each trial

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.

(a) The first trial results in outcome 1;

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

## Answer to relevant Questions

A and B play a series of games. Each game is independently won by A with probability p and by B with probability 1 − p. They stop when the total number of wins of one of the players is two greater than that of the other ...Let S = {1, 2, . . . , n} and suppose that A and B are, independently, equally likely to be any of the 2n subsets (including the null set and S itself) of S. (a) Show that Let N(B) denote the number of elements in B. Use (b) ...Independent trials that result in a success with probability p are successively performed until a total of r successes is obtained. Show that the probability that exactly n trials are required is Use this result to solve the ...In Laplace’s rule of succession (Example 5e), show that if the first n flips all result in heads, then the conditional probability that the next m flips also result in all heads is (n + 1)/(n + m + 1). Five distinct numbers are randomly distributed to players numbered 1 through 5. Whenever two players compare their numbers, the one with the higher one is declared the winner. Initially, players 1 and 2 compare their ...Post your question