If the local professional basketball team, the Sneakers, wins today\'s game, the
ID: 3113647 • Letter: I
Question
If the local professional basketball team, the Sneakers, wins today's game, they have a 2/3 chance of winning their next game. If they lose this game, they have a 1/2 chance of winning their next game. (a) Make a Markov chain for this problem: give the matrix of transition probabilities and draw the transition diagram. (b) If there is a 50-50 chance of the Sneakers winning today's game, what are the chances that they win their next game? (c) If they won today, what are the chances of winning the game after the next?Explanation / Answer
(b)
Case 1: sneakers wins today' game
Probability of wining next game = Prob of winning today game X prob of winning next game given today game won
Case 2: sneakers loses today' game
Probability of wining next game = Prob of losing today game X prob of winning next game given today game loss
Probability of winning next game = 1/2 * 2/3 + 1/2 * 1/2 = 7/12
(c)
sneakers wins today' game
Probability of wining next game = prob of winning next game given today game won = 2/3