Question

If you flip a fair coin $4$ times, what is the probability that you will get exactly $2$ tails?

Answer 1

Use the definition of probability:

A coin is tossed $4$ times.

Write the sample space of $S$ as:

$S=\left\{HHHH,HHHT,HHTH,HTHH,THHH,HHTT,HTHT,THHT,TTTH,TTHT,THTT,HTTT,HTTH,THTH,TTHH,TTTT\right\}$

Therefore $n\left(S\right)=16$

Let A be the event of getting exactly $2$ tails,

Therefore, A can be written as:

$A=\left\{HHTT,TTHH,THTH,HTHT,HTTH,THHT\right\}$

Therefore, $n\left(A\right)=6$

Write the probability as shown:

$$\begin{gathered} p\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)} \\ p\left(A\right)=\frac{6}{16} \\ p\left(A\right)=\frac{3}{8} \end{gathered}$$

Therefore, the probability of getting $2$ tails is $\frac{\mathbf{3}}{\mathbf{8}}.$