A squash match is won when one player wins three games. This situation is often referred to as winning the "best-three-out-of-five" Barbara has a slight edge in winning each game with the odds in favour of 5 to 4
a) what is the probability that maria will win in three straight games?
b) what is the probability of barbara's winning the match?
P=favorable outcomes / possible outcomes
5:4 = 5 / (5+4) = 5/9
(5/9)*(5/9)*(5/9) = 125/729, which is as simple as it goes as far as i know.
as for part b,
i am not sure, and so i will refrain from answering because i will likely be wrong
thank you!
To answer these questions, we can use probability theory.
a) To calculate the probability that Maria will win in three straight games, we need to multiply the probability of Maria winning each individual game. Given that Maria has a slight edge with the odds in favor of 5 to 4, we can assign the probability of Maria winning a game as 5/9 (since 5 out of 9 possible outcomes favor Maria winning).
Thus, the probability of Maria winning in three straight games is given by (5/9) * (5/9) * (5/9), which simplifies to (125/729) or approximately 0.1713.
b) To calculate the probability of Barbara winning the match, we need to consider different possible scenarios:
1. Barbara wins in three straight games: This has a probability of (4/9) * (4/9) * (4/9), as Barbara is favored with odds of 4 to 5. Simplifying gives (64/729).
2. Barbara wins in four games: There are several ways this can happen: (1) Barbara wins the first three games with the probability of (4/9) * (4/9) * (4/9) = (64/729), and then Maria wins the fourth game with probability (5/9). This gives a total probability of (64/729) * (5/9). (2) Barbara wins the first two games with probability (4/9) * (4/9), and then Maria wins the third game with probability (5/9). In the fourth game, Barbara wins with probability (4/9), giving another scenario with total probability of (4/9) * (4/9) * (5/9) * (4/9). We can have other similar scenarios for Barbara winning in four games, each with a probability, respectively, of (64/729) * (5/9), (4/9) * (4/9) * (5/9) * (4/9), and so on.
3. Barbara wins in five games: This means that Barbara loses the first game but wins the next three games, followed by Maria losing the fifth game. The probability for this scenario is: (5/9) * (4/9) * (4/9) * (4/9) * (4/9).
To get the probability of Barbara winning the match, we add up the probabilities of all the scenarios where Barbara wins, which gives us:
(64/729) + (64/729) * (5/9) + (4/9) * (4/9) * (5/9) * (4/9) + (5/9) * (4/9) * (4/9) * (4/9) * (4/9).
By calculating this expression, we can determine the probability of Barbara winning the match.