5: In the best-of -five hockey series , the probability of winning the next game increases for each team by 0.1 if the previous game was won. If the teams ,the Ironmen and the Mustangs ,are in such a series and at the start of the series are evenly matched, what is the probability that (a) the ironmen will win in three straight? (b) the Mustang win the series?
I will be happy to critique your thinking.
+bobpursley you didn't answer Samir's question lol
lol I answered after 8 years. Such long history
To find the probability of the Ironmen winning in three straight games, we can use the concept of conditional probability.
(a) The Ironmen winning in three straight means that they have to win the first game, then the second game, and finally the third game.
Since the probability of winning the next game increases by 0.1 if the previous game was won, the probability of the Ironmen winning the first game is 0.5 (evenly matched). The probability of winning the second game, given that they won the first, is 0.5 + 0.1 = 0.6. Similarly, the probability of winning the third game, given they won the first two, is 0.6 + 0.1 = 0.7.
To find the probability that all three events happen, we multiply the probabilities together: 0.5 * 0.6 * 0.7 = 0.21.
Therefore, the probability that the Ironmen win in three straight games is 0.21.
(b) To find the probability of the Mustangs winning the series, we need to consider the different ways in which they can win.
The Mustangs can win in three straight games, which means the Ironmen would not win any games. Using the same reasoning as above, the probability of the Mustangs winning in three straight games is 0.5 * 0.6 * 0.7 = 0.21 (same as the Ironmen winning in three straight).
The Mustangs can also win in four games if they win the first three and lose the fourth. The probability of this happening is the Ironmen losing the first three games (0.5 * 0.4 * 0.3) multiplied by the probability of winning the fourth game (0.5). So, the probability of the Mustangs winning in four games is 0.06.
The last possibility is the Mustangs winning in five games. This means that they would have to lose the first two games, win the third, lose the fourth, and win the fifth. The probability of this happening is the Ironmen winning the first two games (0.5 * 0.4), multiplied by the probability of the Mustangs winning the third game (0.6), multiplied by the probability of the Ironmen winning the fourth game (0.5), multiplied by the probability of the Mustangs winning the fifth game (0.7). Therefore, the probability of the Mustangs winning in five games is 0.04.
To find the overall probability of the Mustangs winning the series, we add up the probabilities of each possibility: 0.21 + 0.06 + 0.04 = 0.31.
Therefore, the probability that the Mustangs win the series is 0.31.