Odds in favour

[mmk]

Suppose the odds of the TorontoMaple Leafs winning the Stanley Cup are1:5, while the odds of the MontréalCanadiens winning the Stanley Cup are2:13. What are the odds in favour of eitherToronto or Montréal winning the StanleyCup? i dont have an idea of what to do here?

 

[khansaheb]

Suppose the odds of the TorontoMaple Leafs winning the Stanley Cup are1:5, while the odds of the MontréalCanadiens winning the Stanley Cup are2:13. What are the odds in favour of eitherToronto or Montréal winning the StanleyCup? i dont have an idea of what to do here?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[Dr.Peterson]

Suppose the odds of the TorontoMaple Leafs winning the Stanley Cup are1:5, while the odds of the MontréalCanadiens winning the Stanley Cup are2:13. What are the odds in favour of eitherToronto or Montréal winning the StanleyCup? i dont have an idea of what to do here?

I would first translate from odds into probabilities, and then consider the rule for "or" in probabilities. What have you learned about that?

 

[The Highlander]

The OR rule in probability is explained here (in just the terms you are looking for too ).

Further information (eg: on the AND rule) is also available by following the links on the left-hand side of that web page.

Hope that helps.

 

[Steven G]

What is the probability that both teams win the Stanley Cup??

 

[The Highlander]

What is the probability that both teams win the Stanley Cup??

That 'issue' is addressed in the explanation of the OR rule.

 

[Steven G]

That 'issue' is addressed in the explanation of the OR rule.

That is correct. You slipped in that AND without my seeing it.

 

[Agent Smith]

If there are a total of [imath]5[/imath] outcomes, and if the number of possible ways to win = [imath]2[/imath] and the number of ways to lose = [imath]3[/imath], the Odds of winning are [imath]2:3[/imath].

 

[Steven G]

If there are a total of [imath]5[/imath] outcomes, and if the number of possible ways to win = [imath]2[/imath] and the number of ways to lose = [imath]3[/imath], then Odds of winning are [imath]2:3[/imath].

What are the 5 outcomes and why exactly 3 ways to win?

 

[The Highlander]

If there are a total of [imath]5[/imath] outcomes, and if the number of possible ways to win = [imath]2[/imath] and the number of ways to lose = [imath]3[/imath], the Odds of winning are [imath]2:3[/imath].

I'm not sure I understand the point of your post.

Could you. perhaps, explain it and its relevance to this thread?

Thanks.

 

[Steven G]

I'm not sure I understand the point of your post.

Could you. perhaps, explain it and its relevance to this thread?

Thanks.

There are nothing but If's in the post. The conclusion does follow but as you said, is it relevant to this thread?

 

[Dr.Peterson]

I'm not sure I understand the point of your post.

Could you. perhaps, explain it and its relevance to this thread?

Thanks.

There are nothing but If's in the post. The conclusion does follow but as you said, is it relevant to this thread?

My understanding is that he is trying to explain what "odds" means, in case that is the OP's difficulty.

We have no idea yet what sort of help is actually needed.

 

[Agent Smith]

My understanding is that he is trying to explain what "odds" means, in case that is the OP's difficulty.

We have no idea yet what sort of help is actually needed.

Herr Doktor, correct diagnosis!

I'm not sure I understand the point of your post.

Could you. perhaps, explain it and its relevance to this thread?

Thanks.

There are nothing but If's in the post. The conclusion does follow but as you said, is it relevant to this thread?

I came to the, mayhaps erroneous, conclusion that the OP needed clarity on what odds mean.

Gracias for your questions.

 

[mmk]

I would first translate from odds into probabilities, and then consider the rule for "or" in probabilities. What have you learned about that?

ohh so you would do 1/1+5 and 2/13+2 and thats 1/6 and 2/15 but then u have to add it so it would be 3/10 and then do 10-3= 7 so 3:7 right

 

[The Highlander]

I came to the, mayhaps erroneous, conclusion that the OP needed clarity on what odds mean.

It's been a week now since the original post and there's been no further contribution from the original poster, so I expect s/he was given an answer s/he was happy with elsewhere or has just lost interest so it doesn't matter much whether your post caused any confusion or not.

As was mentioned earlier, what she really needed (if anything) was advice on how to convert odds into probabilities so that the original query might be answered using P(A or B), the probability that one of two mutually exclusive events might occur given that the probability of each occurring separately is known.

The the odds of the Toronto Maple Leafs winning the Stanley Cup were given as 1:5, so the probability of that event occuring would be: \(\displaystyle \frac{1}{6}\) (let's call that A) whilst the odds of the Montréal Canadiens winning the Stanley Cup were given as 2:13, so the probability of that event occuring would be: \(\displaystyle \frac{1}{15}\) (let's call that B).

P(A or B) ≡ P(A) + P(B) = \(\displaystyle \frac{1}{6}+\frac{1}{15}=\frac{7}{30}\) (in this case).​

Therefore, the odds of one of those two teams winning the Stanley Cup (in the situation presented to us) would be 7:23.

(Since both 7 and 23 are prime numbers those odds cannot be simplified or made to look any prettier! )

 

[Dr.Peterson]

ohh so you would do 1/(1+5) and 2/(13+2) and thats 1/6 and 2/15 but then u have to add it so it would be 3/10 and then do 10-3= 7 so 3:7 right

Yes, that's right. TH made a small mistake to keep you thinking

 

[The Highlander]

Yes, that's right. TH made a small mistake to keep you thinking

Nope! It was just carelessness on my part!

(I need to take a leaf out of your book and start doing everything at least two different ways to arrive at the same answer before accepting it as correct. )

I should, of course, have said...

"The the odds of the Toronto Maple Leafs winning the Stanley Cup were given as 1:5, so the probability of that event occurring would be: \(\displaystyle \frac{1}{6}\) (let's call that A) whilst the odds of the Montréal Canadiens winning the Stanley Cup were given as 2:13, so the probability of that event occurring would be: \(\displaystyle \frac{2}{15}\) (let's call that B).​

​

P(A or B) ≡ P(A) + P(B) = \(\displaystyle \frac{1}{6}+\frac{2}{15}=\frac{9}{30}=\frac{3}{10}\) (in this case).​

​

Therefore, the odds of one of those two teams winning the Stanley Cup (in the situation presented to us) would be 3:7."​