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# S1: Independent probability question - easier method? watch

1. It is estimated that the probability of a league cricket match ending in a home win is 0.4, an away win is 0.25, and a draw is 0.35. Find the probability that if the three games are played, and the results are independent, there will be exactly one home win.
My method is shown below. I got the answer correct but I want to know if there is an easier, more methodical way to go about it?

I did realise at the end that you could just multiply all of the probabilities of a win at home happening first by 3, but I'm wondering if there's a better way to do it.

2. I think you need to post more of the question. From what you've posted, they might only play home games, or away games, or anything in between. It's also not clear whether the p(draw) =0.35 is supposed to apply to both home+away games or only away games.

That said, it looks like you could make a significant simplification by noting that we dont have to care about the difference between draws and losses to answer the question.
3. (Original post by DFranklin)
I think you need to post more of the question. From what you've posted, they might only play home games, or away games, or anything in between. It's also not clear whether the p(draw) =0.35 is supposed to apply to both home+away games or only away games.

That said, it looks like you could make a significant simplification by noting that we dont have to care about the difference between draws and losses to answer the question.
Sorry about the confusion, here's a picture of the full question.

(I think that when they say a 'home win', they just mean the probability of a win from the team that is playing at their own grounds, a.k.a the home team. Similarly for an 'away win', the probability of a win from the team that is playing at their opponents grounds, a.k.a the away team.)
4. Yeah, your original question wasn't actually that differemt but the extra "the" really threw me. (My assumption you were talking about a particular team, not the match).

With that cleared up, for (b), you can answer quickly using binomial and my previous comment.

For (c) Calculate the probability of home win, away win, draw (in that order), and then multiply by the number of possible different orders.
5. Personally I would do a Tree diagram for a question likes this as it maps it out and makes it easier for you to get the answer.
6. (Original post by M4cc4n4)
Personally I would do a Tree diagram for a question likes this as it maps it out and makes it easier for you to get the answer.
Note that there are 27 entries in a complete tree diagram for this question (39 if you include non-leaf nodes).
7. thank goodness I don't have to do S1 again then
8. (Original post by DFranklin)
Note that there are 27 entries in a complete tree diagram for this question (39 if you include non-leaf nodes).
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