The probability of the team winning its next game is 0.733
Since we are assuming that each the three outcomes are equally likely, hence outcome will have a probability of 1/3
Let:
Win = W ; Lose = L
Probability of winning next game :
If LL = 90%
If LW = 50%
If WW = 90%
Therefore,
The probability of the winning its next game :
[P(wining next game) × P(LL) + P(wining next game) × P(LW) + P(winning next game) × P(WW)]
[(0.8 × 1/3) + (0.5 × 1/3) + (0.9 × 1/3)] = 0.7333
Hence, the probability of the team winning it's next game is 0.733.
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