Answer :
If the team has probabilities 0.5, 0.1, and 0.4 of a win, tie, or loss for their first game respectively, then the probability that they will win their third game 0.526.
In the given question,
If the team has respective probabilities 0.4, 0.5, and 0.1 of a win, tie, or loss for their first game respectively, then we have to find the probability that they will tie their third game.
We obtain the two step transition probability matrix here as:
P^2 = [tex]\left [ \begin{matrix}0 &0 &1 \\ 0.1 &0.5 &0.4 \\ 0.9 &0.1 &0 \end{matrix} \right ]\left [ \begin{matrix}0 &0 &1 \\ 0.1 &0.5 &0.4 \\ 0.9 &0.1 &0 \end{matrix} \right ][/tex]
P^2 = [tex]\left [ \begin{matrix}0.9 &0.1 &0 \\ 0.41 &0.29 &0.3 \\ 0.01 &0.05 &0.94 \end{matrix} \right ][/tex]
Using this, for the given current probability vector of (0.1, 0.5, 0.4) for loss, tie and win respectively, we get the final vector as:
bP^2 = (0.1, 0.5, 0.4) [tex]\left [ \begin{matrix}0.9 &0.1 &0 \\ 0.41 &0.29 &0.3 \\ 0.01 &0.05 &0.94 \end{matrix} \right ][/tex]
bP^2 = (0.299, 0.175, 0.526)
Therefore probability that win the third game is given here as: 0.526.
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The right question is:
A football team either wins, ties, or losses 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 0.4 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 0.9. Write all answers as integers or decimals.
If the team has respective probabilities 0.4, 0.5, and 0.1 of a win, tie, or loss for their first game respectively, what is the probability that they will tie their third game?
