Question

Exercise: Frequency interpretations 0.0/2.0 points (ungraded) Jack is a gambler who pays for his MIT tuition by spending weekends in Las Vegas. His latest game of choice is blackjack, which he plays using a fixed strategy. However, at this special blackjack table, the dealer uses one of 2 decks of cards for each hand. Using his fixed strategy, Jack wins with probability 7/15 when deck #1 is used and with probability 4/9 when deck #2 is used, whenever deck #1 is used, ifjack wins, the dealer switches to deck #2 for the next hand, and if Jack loses, the dealer keeps using deck #1 for the next hand. Whenever deck #2 is used fjack wins. the dealer keeps using deck #2 for the next hand, and ifjack loses, the dealer switches to deck #1 for the next hand. Jack's wins and losses can be modeled as the transitions of the following Markov chain, whose states correspond to the particular deck being used (win) 2 ) ) (win) (loss) What is Jack's long-term probability of winning?

Answer 1

0.45652