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tough probability problem

Mathematics
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1 Attachment
on c)
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why is it (1+p)^(m-r) instead of (p)^(m-r)

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Other answers:

@zarkon, when you come on can you take a look?
whew i can explain that one (and not embarrass myself) because it is algebra
the probability that you decide to buy a ticket and it loses is \(\frac{1-p}{2}\) viewing this as bernoulli trials (independent repeated experiments with only two outcome) the the formula is \[P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}\] but in this case \[p=\frac{1-p}{2}\] and therefore \[1-p=1-\frac{1-p}{2}=\frac{1+p}{2}\]
i guess what i wrote is silly, i should have made the first \(p\) a \(p^*\) or some other variable
I see, all those 'p' were confusing me
thanks for your help
yw

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