A player plays a game in which, during each round, he has a probability 0.55 of winning $1 and probability 0.45 of losing $1. These probabilities do not change from round to round, and the outcomes of rounds are independent. The game stops when either the player loses its money, or wins a fortune of $M. Assume M = 5, and the player starts the game with $1. (a) Model the player's wealth as a Markov chain and construct the probability transition matrix (b) What is the probability that the player goes broke after 3 rounds of play?

An engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 120 lb and 161 lb. the new population of pilots has normally distributed weights with a mean of 125 lb and a standard deviation of 28.1 lb. a)if a pilot is randomly selected, find the probability that his weight is between 120 lb and 161 lb.the probability is approximately? b. if 36 different pilots are randomly selected, find the probability that their mean weight is between 120 lb and 161 lb. the probability is approximately? c. when redesigning the ejection seat, which probability is more relevant? . part (b) because the seat performance for a single pilot is more important. b. part (b) because the seat performance for a sample of pilots is more important. c. part (a) because the seat performance for a sample of pilots is more important. d. part (a) because the seat performance for a single pilot is more important.