The probability of obtaining exactly 7 heads when flipping 8 coins can be deduced using the binomial probability
The formula for the binomial probability, P, is
[tex]P_x=(^n_x)p^xq^{n-x}[/tex]
Where
[tex]\begin{gathered} n=8 \\ x=7 \\ p=\frac{1}{2} \\ q=1-p=1-\frac{1}{2}=\frac{1}{2} \\ \text{Bceause when you flip a coin, you either get a head or a tail} \\ \text{Thus the proability of getting a head or tail i.e p or q is }\frac{1}{2} \end{gathered}[/tex]
Substitute the values into the formula for binomial probability
[tex]\begin{gathered} P_x=(^n_x)p^xq^{n-x} \\ P_7=^8C_7\times(\frac{1}{2})^7\times(\frac{1}{2})^{8-7}_{} \\ P_7=8\times\frac{1}{128}\times\frac{1}{2}=\frac{8}{256}=\frac{1}{32} \\ P_7=\frac{1}{32} \end{gathered}[/tex]
Hence, the probability of obtaining exactly 7 heads when flipping 8 coins is 1/32 (in fractions)
