As written there is absolutely no way that question has an answer.You are part of a football team, there are 3 possible outcomes for each match win ; lose or draw. what is the probability of winning the next 2 matches in a row?
Why do you say that? I think it meant to assume the likelihood of each event of winning, losing, and drawing is equally likely. Also, each game is assumed to be independent.As written there is absolutely no way that question has an answer.
For the exact reason: "nothing is given about the chances," the equally likely assumption would be fair. Don't you think? (given if that's the exact wording of the original problem, and that's all you have to go on)Because nothing is given about the chances, why would assume anything?
Do you really think it's reasonable to suppose those three outcomes are equally likely? It's somewhat like supposing that heads, tails, and edge are equally likely in tossing a coin.For the exact reason: "nothing is given about the chances," the equally likely assumption would be fair. Don't you think? (given if that's the exact wording of the original problem, and that's all you have to go on)
As written there is absolutely no way that question has an answer.
pka wrote that post because the problem can't be done. If two people sit down at a blackjack table do they both have the same chance of winning?For the exact reason: "nothing is given about the chances," the equally likely assumption would be fair. Don't you think? (given if that's the exact wording of the original problem, and that's all you have to go on)
We don't know for sure, and maybe they have equal chances of winning; perhaps one is better than the other. How do you know for sure without historical experience? But it would be a fair initial assumption to say A has an equal chance of winning as B. Why would it be unfair to say they have equal chances of winning without knowing anything about them?pka wrote that post because the problem can't be done. If two people sit down at a blackjack table do they both have the same chance of winning?
To answer your question, yes, I think it's a reasonable assumption to make as we know nothing about the football team's winning records. As we observe more games, with historical experience, we can update our initial beliefs. This idea follows Bayesian Inference, where we make a particular assumption about our model and update it with more information.Do you really think it's reasonable to suppose those three outcomes are equally likely? It's somewhat like supposing that heads, tails, and edge are equally likely in tossing a coin.
If we assume that Team 1 and Team 2 are equally matched, then Team 1 has Pr(win)=Pr(lose)=Pr(draw)=1/3. Similarly, for Team 2. I don't see why "we cannot assume that one-third of games end with a draw."?Even if we can assume that the teams are equally matched, we cannot assume that one third of games end with a draw.
You're making an assumption this is American football; it can be soccer.The scoring system may make a draw unlikely https://www.bbc.co.uk/sport/american-football/tables
You could suppose that, for the sake of argument, and state it up front when you write up your answer. But to assume that it is true is not reasonable.If we assume that Team 1 and Team 2 are equally matched, then Team 1 has Pr(win)=Pr(lose)=Pr(draw)=1/3. Similarly, for Team 2. I don't see why "we cannot assume that one-third of games end with a draw."?
No, what you say is not true at all.The crux of the issue lies in how probability is presented, at least at the introductory level.
Using the classic coin toss example: "A coin has two possible outcomes, head or tail. What's the probability of getting two heads in a row?"
When presented with such questions, are students being taught to ask the question: "Is it a fair coin or is it loaded" (as most of you suggested, and the correct way) OR
Are they being taught to ignore that question and proceed with the calculation with their common understanding a coin has two sides, therefore Pr(Head)=Pr(Tail)=1/2?
I think you would agree, like it or not; the latter is most likely the standard practice. As a result, the "common practice" is to assume the outcomes are equally likely, unless stated otherwise in such problems.
With all that said, it boils down to the precision of the educators and question's author.