Question

What is the probability of flipping a coin seven times and getting at least 4 heads?

Answer 1

4 out of 7 aka 4/7

Answer 2

Have you learned about the binomial distribution?

Answer 3

@SithsAndGiggles Not yet

Answer 4

It's easier to compute the probability with a calculator if you had learned it, assuming you know how to type a series into a calculator... no matter, here's what you'd be doing anyway:
\[\begin{align*}P(\text{at least 4 heads})&=P(\text{4 heads})+P(\text{5 heads})+P(\text{6 heads})+P(\text{7 heads})\\
&=\frac{\begin{pmatrix}7\\4\end{pmatrix}}{2^7}+\frac{\begin{pmatrix}7\\5\end{pmatrix}}{2^7}+\frac{\begin{pmatrix}7\\6\end{pmatrix}}{2^7}+\frac{\begin{pmatrix}7\\7\end{pmatrix}}{2^7}\\\\\\
&=\cdots
\end{align*}\]
where \(\begin{pmatrix}n\\k\end{pmatrix}={}_nC_k=\dfrac{n!}{k!(n-k)!}\).

Answer 5

@SithsAndGiggles Ah, I think I get it now. Thanks!!

Answer 6

yw!