Question

anybody knows how to solve this question? a large group of people gets together, each one flips two coins 160 times and counts the number of double heads. about what percentage of these people should get counts in the range 35 and 45.

Answer 1

find attached my approach to the solution. Come back to me if any doubt

Answer 2

got it. thank you very much.

Answer 3

you are welcome

Answer 4

OH MY DEAR FRIEND do u know how the binomial expansion came about

Answer 5

@dan815 I do not get your question

Answer 6

oh sorry i was just asking you if u knew how that binomial distribution formula came about

Answer 7

@dan815
The formula rationale is quite simple. Imagine you want a determined sequence of events when you repeat an experiment on a population. We have the following cases when flipping once:
HH HT TH TT, teherefore the prob of HH is 0.25 (one case out of four). For the other events (HT TH TT) we do not really care about the combination, the only requirement is no double heads, that is 0.75 (3 cases out of four or 1-0.25)
Now imagine we flip two coins 5 times and we want to know the probability of getting 3 double heads. One sequence might be: HH HH HH HT TH whose probability is:\[0.25^3 \times 0.75^2\].But this is valid for one sequence and we know that the number of sequences containing 3 double heads is given by:\[\left(\begin{matrix}5 \\3\end{matrix}\right)\] what means that the total probability is \[\left(\begin{matrix}5 \\ 3\end{matrix}\right)0.25^3 \times 0.75^2\]. In general we can say that:\[P(k)=\left(\begin{matrix}n \\ k\end{matrix}\right)p^k(1-p)^{n-k}\]

Answer 8

aw so u already knew :P i was gonna show off lol

Answer 9

soo then how about this part, do u know how to calculate the value of P(k) for Summation 35 - 45