Probability of scoring goal.

[kuba99]

I have a problem with this example, because I know what I should do to solve this, but i have no idea haw I can do this (a lot of sense for sure).

 

[Steven G]

You really should define your variables. To be honest it is rude no to as the readers have to spend time trying to figure out what your variables means when you can simply state the definition. Not a big problem, just try to define them in the future.

I suspect that w means win. Based on P(s) = .25 I would assume that s means Bayern wins and Lewandowski scores at least one goal but I do not think that you mean that. I think that you think that s means that Lewandowski scores.

Please clearly state your variables and do as much of the work you can and then we'll push you further toward the answer.

 

[Dr.Peterson]

First, let's check how you have defined the events. The problem was:

Probability that Bayern Monachium wins an away match is equal to 0.6.​

Probability that Bayern Monachium wins a match and Lewandowski scores at least one goal is equal to 0.25.​

What is the probability that Lewandowski scores in an away match under the condition that Bayern wins the match?​

You wrote:

P(W) = 0.6​

P(S) = 0.25​

P(W∩S) = P(0.6∩0.25)​

P(S|W) = ?​

But you surely meant to define

W = Bayern Monachium wins an away match​

S = Lewandowski scores at least one goal​

If so, then it is not true that P(S) = 0.25. What is the probability that equals 0.25?

Also, note that P(0.6∩0.25) is meaningless; what goes inside the parenthesis is an event, not a couple numbers connected with "and".

Note: This is essentially what Jomo said, but since I put in the time to transcribe the problem and work (which you could have done, to make it easier for us to interact with you), I'm still posting it.

Once you get the statements right, you will want to express them in terms of the definition of conditional probability, and will almost have the answer.

 

[kuba99]

W = Bayern Monachium wins an away match
S = Lewandowski scores at least one goal
exactly, I am begging for my lack of professionalism, but at my place it is already 3.20 am, and I am a bit tired , but thank you, I will remember to describe variables! I would not like to be unpleasant, of course I greatly appreciate your help @Jomo @Dr.Peterson

 

[pka]

W = Bayern Monachium wins an away match
S = Lewandowski scores at least one goal
exactly, I am begging for my lack of professionalism, but at my place it is already 3.20 am, and I am a bit tired , but thank you, I will remember to describe variables! I would not like to be unpleasant, of course I greatly appreciate your help @Jomo @Dr.Peterson

\(\displaystyle \mathcal{P}(S|W)=\frac{\mathcal{P}(S\cap W)}{\mathcal{P}(W)}=~?\)

 

[Steven G]

Of course you are not trying to be unpleasant. One thing we try very hard to teach on this forum is to write/speak mathematics correctly.
So please state what equals .6, what equals .25 and what you are being asked for. Once you get there either you will see the answer or will need a little nudge.

 

[kuba99]

P(W) = 0.6 - Bayern Monachium wins an away match
P(S) = 0.25 - Lewandowski scores at least one goal

Answer: P(S|W) = 0.25/0.6 = 5/12

Sometimes I just have to read the exercise 3 or 4 times, and everything will be easy, but I often forget about it ... once again thank you for your help and for helping me open my mind for some problems ?
I really appreciate what you do, gentlemen @pka @Jomo @Dr.Peterson

 

[Steven G]

Sorry but P(S) is NOT .25.

Please re-read what equals .25 and what you called S

 

[Dr.Peterson]

Since you said you're tired, I'll give you the answer to my question.

The problem was:

Probability that Bayern Monachium wins an away match is equal to 0.6.​

Probability that Bayern Monachium wins a match and Lewandowski scores at least one goal is equal to 0.25.​

What is the probability that Lewandowski scores in an away match under the condition that Bayern wins the match?​

P(W) = 0.6 - Bayern Monachium wins an away match
P(S∩W) = 0.25 - Bayern Monachium wins an away match and Lewandowski scores at least one goal

Now write the equation pka gave you, filling in these facts ...

 

[Steven G]

I now think that this problem is not valid and here is why.
We are told that Probability that Bayern Monachium wins an away match is equal to 0.6 and the Probability that Bayern Monachium wins a match and Lewandowski scores at least one goal is equal to 0.25.
The problem is that it does not say Probability that Bayern Monachium wins an away match and Lewandowski scores at least one goal is equal to 0.25 .

But of course kuba99 should assume that it does say "wins an away match" just to do the exercise.

 

[Dr.Peterson]

Yes, I observed that when I first read the problem, and chose not to complicate things with reality. But it's worth a mention at some point.