# Question: A and B flip coins A starts and continues flipping

A and B flip coins. A starts and continues flipping until a tail occurs, at which point B starts flipping and continues until there is a tail. Then A takes over, and so on. Let P1 be the probability of the coin’s landing on heads when A flips and P2 when B flips. The winner of the game is the first one to get

(a) 2 heads in a row;

(b) A total of 2 heads;

(c) 3 heads in a row;

(d) A total of 3 heads.

In each case, find the probability that A wins.

(a) 2 heads in a row;

(b) A total of 2 heads;

(c) 3 heads in a row;

(d) A total of 3 heads.

In each case, find the probability that A wins.

**View Solution:**## Answer to relevant Questions

Die A has 4 red and 2 white faces, whereas die B has 2 red and 4 white faces. A fair coin is flipped once. If it lands on heads, the game continues with die A; if it lands on tails, then die B is to be used. (a) Show that ...Consider a collection of n individuals. Assume that each person’s birthday is equally likely to be any of the 365 days of the year and also that the birthdays are independent. Let Ai,j, i ≠ j, denote the event that ...A bag contains a white and b black balls. Balls are chosen from the bag according to the following method: 1. A ball is chosen at random and is discarded. 2. A second ball is then chosen. If its color is different from that ...(a) An urn contains n white and m black balls. The balls are withdrawn one at a time until only those of the same color are left. Show that, with probability n/(n + m), they are all white. Imagine that the experiment ...A gambling book recommends the following “winning strategy” for the game of roulette: Bet $1 on red. If red appears (which has probability 18/38), then take the $1 profit and quit. If red does not appear and you lose ...Post your question