Question

An unbiased coin is tossed four times. Find the probability of the given event. The coin lands heads more than once.

Answer 1

`\mathbb P(X>1)=1-\mathbb P(X\le1)=1-\mathbb P(X=0)-\mathbb P(X=1)`

The coin is unbiased, so either side has the same probability of
`\frac12` of occurring, where


`\mathbb P(X=x)=\dbinom4x\left(\frac12\right)^x\left(\frac12\right)^(4-x)=\dbinom4x\left(\frac12\right)^4=\frac1{16}\dbinom4x`

So the probability of getting heads more than once is


`\mathbb P(X>1)=1-\frac1{16}\dbinom40-\frac1{16}\dbinom41=(11)/(16)`