I've got two questions:

1. A mother knows that 20% of children who accept invitation to birthday parties do not come. If she invites 12 children to a party and only has 10 party hats, what is the probability that there is not a hat for every child who comes?

The mother knows that there is a probability of 0.1 that a child who comes refuses to wear a hat. if this is taken into account, what is the probability that the number of hats will not be adequate?

I know that the probability of a child not coming is $\displaystyle \frac{1}{5}$. So the probability that 11 or 12 come will be

$\displaystyle P(not enough hats)=(\frac{4}{5})^{11}(\frac{1}{5})+(\frac{4}{5} )^{12}=0.0859$ the answer for this part is supposed to be 0.28, without the first part i don't see that the second part can be done.

2.When a boy fires a rifle at a range the probability that he hits the target isp.

(a) Find the probability that, firing 5 shots, he scores at least 4 hits.

(b) Find the probability that, firingnshots $\displaystyle (n\geq2)$, he scores at least two hits.

For (a), there would be the probability of hitting 4 or 5 times. $\displaystyle p^4(1-p)+p^5=p^4$ which is not the answer. Answer is [tex]5p^4-4p^5[\math]

(b) answer would be 1 minus the probability of missing all and hitting 1.

[tex]1-p(1-p)^{n-1}-(1-p)^n[\math]. answer is $\displaystyle 1-np(1-p)^{n-1}-(1-p)^n$.

For all of these where have i got wrong?

Thanks for any help!