A dodgeball team either wins, ties, or loses each game. If they lose a game, the

Question

A dodgeball team either wins, ties, or loses each game. If they lose a game, their probability of winning the next game is 1 and their probability of losing the next game is 0. If they tie a game, their probability of winning the next game is 0.8 and their probability of losing the next game is 0.1. If they win a game, their probability of winning the next game is 0 and their probability of losing the next game is 0.2. Write all answers as integers or decimals.

If the team has respective probabilities 0.7, 0.1, and 0.2 of a win, tie, or loss for their first game, what is the probability that they will win their second game?



If the team has probabilities 0.7, 0.1, and 0.2 of a win, tie, or loss for their first game respectively, what is the probability that they will tie their third game?



If the team has probabilities 0.7, 0.1, and 0.2 of a win, tie, or loss for their first game respectively, what is the probability that they will lose their fourth game??

Explanation / Answer

here initial vector A =[ 0.7 0.1 0.2]

and transition matrix: Q:

therefore vector for second game A1 =A*Q =[0.25 0.57 0.15]

a)  probability that they will win their second game =0.25

b)

vector for second game A2 =A1*Q =[0.606 0.281 0.113]

probability that they will tie their third game =0.281

c)

vector for fourth game A3 =A2*Q =[0.3378 0.5129 0.1492]

probability that they will lose their fourth game=0.1492

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