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## Homework Statement

A football team wants to have a 0,5 chance of scoring on at least 4 out of 5 penalties. What must be the probability p of scoring on each penalty?

## Homework Equations

[tex]{n \choose k} \cdot p^k \cdot (1-p)^{n-k}[/tex]

## The Attempt at a Solution

Tried this:

[tex]{5 \choose 4} \cdot p^4 \cdot (1-p)^{1} \ + \ {5 \choose 5} \cdot p^5 \cdot (1-p)^{0} = 0,5[/tex]

[tex]5 \cdot p^4 \cdot (1-p) + 1 \cdot p^5 \cdot 1 = 0,5[/tex]

[tex]5p^4 - 5p^5 + p^5 = 0,5[/tex]

[tex]5p^4 - 4p^5 = 0,5[/tex]

I don't know what to do with this equation, although someone told me about Newton's approximation something. That is way above the level of this math course anyway, so I guess there is a much easier way to solve this problem. Kinda embarrassing, really, as I take a higher course but came across this problem when helping a younger student.

Hoping for all the help I can get. :-) Thanks a lot!

Damn, I don't know what's up with the Latex, but never mind that long, stupid string on the top. Apparently there's something wrong with the spacing, and it won't go away even though I remove it all.

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