Example 2.2 Two desperados A and B are playing Russian roulette, and they have agreed that they will take turns pulling the trigger of a revolver with six cylinders and one bullet. This dangerous game ends when the trigger has been pulled six times without a fatal shot occurring (after each attempt the magazine is spun to a random position). Desperado A begins. What is the probability mass function of the number of times desperado A pulls the trigger?

In the game of roulette, a player can place a $9 bet on the number 29 and have a probability of winning. If the metal ball lands on 29, the player gets to keep the 38 1 $9 paid to play the game and the player is awarded an additional $315. Otherwise, the player is awarded nothing and the casino takes the player's $9, Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. The expected value is $.5 (Round to the nearest cent as needed.)

In the game of​ roulette, a player can place a $7 bet on the number 32 and have a 138 probability of winning. If the metal ball lands on 32​, the player gets to keep the ​$7 paid to play the game and the player is awarded an additional ​$245.Otherwise, the player is awarded nothing and the casino takes the​ player's $7. Find the expected value​ E(x) to the player for one play of the game. If x is the gain to a player in a game of​ chance, then​ E(x) is usually negative. This value gives the average amount per game the player can expect to lose.

Target practice: Laura and Philip each fire one shot at a target. Laura has probability G5 of hitting the target, and Philip has probability 0.4. The shots are independent. Round your answers to four decimal places, if necessary. (a) Find the probability that both of them hit the target. (b) Given that Laura hits the target, the probability is 0.2 that Philip's shot hits the target closer to the bull's-eye than Laura's. Find the probability that Laura hits the target and that Philip's shot is closer to the bull's-eye than Laura's shot is. Part: 0/ 2 Part 1 of 2 The probability that both of them hit the target is