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# S1 Probability question watch

1. Hey there

I've literally been trying for days to solve this problem and just can't for the life of me. Any help is much appreciated:

Xavier, Yuri and Zara attend a sports centre for their judo club’s practice sessions. The probabilities of them arriving late are, independently, 0.3, 0.4, and 0.2 respectively.

Zara’s friend, Wei, also attends club practice sessions. The probability that Wei arrives late is 0.9 when Zara arrives late, and is 0.25 when Zara does not arrive late.

Calculate the probability that for a particular practice session, either Zara or Wei, but not both, arrive late.

Once again, any help is much appreciated.
2. I'd say you need to add:
The probability of Zara being late x the probability of Wei not being late
+
The probability of Zara not being late x the probability of Wei being late
Does that make it easier?
3. If I call Z the probability that Zara is late, and W the probability that Wei is late, then you are looking for:

Since Zara and Wei being late are not independent, you will need to use conditional probability to evaluate each of these two terms.

Can you take it from there?
4. Hi there, first of all thanks for your help guys.

However I can't quite take it from there - I get what you are saying and have expanded it using conditional probability:

P(Z n W') + P(Z' n W) = [P(Z) x P(W'|Z)] + [P(W) x P(W|Z')]

Problem is, I can't figure out how I can find P(W'|Z) or P(W) from the information...

It's a tough one for me.
5. (Original post by NuovoVesuvio)
Hi there, first of all thanks for your help guys.

However I can't quite take it from there - I get what you are saying and have expanded it using conditional probability:

P(Z n W') + P(Z' n W) = [P(Z) x P(W'|Z)] + [P(W) x P(W|Z')]

Problem is, I can't figure out how I can find P(W'|Z) or P(W) from the information...

It's a tough one for me.
There are two ways you can split P(Z' n W) into conditional probabilities, and that's neither of them.

You want: P(Z') x P(W|Z')

and you should be able to work out those

[the other one, just for reference, would be P(W) x P(Z'|W)]
6. Thanks for your help mate.

I'm almost there;

[0.2 x P(W'|Z)] + [0.8 x 0.25].

As stated in my last post, I just can't tell how to work out P(W'|Z) from the information given. Sorry to be such a pain!
7. (Original post by NuovoVesuvio)

I'm almost there;

[0.2 x P(W'|Z)] + [0.8 x 0.25].

As stated in my last post, I just can't tell how to work out P(W'|Z) from the information given. Sorry to be such a pain!
"Zara’s friend, Wei, also attends club practice sessions. The probability that Wei arrives late is 0.9 when Zara arrives late, and is 0.25 when Zara does not arrive late."

P(W'|Z) is the probability of Wei not being late, given that Zara has been late. As it says above, when Zara arrives late, the probability that Wei IS late is 0.9, so you use that to find the probability that Wei isn't late. Does that help?

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Updated: April 12, 2009
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