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.

Respuesta :

Answer:

Concept:

If you flip a coin once, there are

[tex]\text{2 possiblities}[/tex]

Using the binomial probability formula below, we will have

[tex]P(x)=^nC_rp^xq^{x-r}[/tex]

Where

[tex]\begin{gathered} p=probability\text{ of success} \\ q=probability\text{ of failure} \end{gathered}[/tex][tex]\begin{gathered} p=\frac{1}{2} \\ q=\frac{1}{2} \\ n=7 \\ x=7 \end{gathered}[/tex]

By substituting the values, we will have

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

Hence,

The final answer is

[tex]\Rightarrow\frac{1}{128}[/tex]