Question

Find the probability of obtaining exactly seven tails when flipping seven coins. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

Concept:

If you flip a coin once, there are

`\text{2 possiblities}`

Using the binomial probability formula below, we will have

`P(x)=^nC_rp^xq^(x-r)`

Where

`\begin{gathered} p=probability\text{ of success} \\ q=probability\text{ of failure} \end{gathered}`
`\begin{gathered} p=(1)/(2) \\ q=(1)/(2) \\ n=7 \\ x=7 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} P(x)=^nC_rp^xq^(x-r) \\ P(x=7)=^7C_7((1)/(2))^7((1)/(2))^(7-7) \\ P(x=7)=((1)/(2))^7 \\ P(x=7)=(1)/(128) \end{gathered}`

Hence,

The final answer is

`\Rightarrow(1)/(128)`