# A coin is tossed 12 times. What is the probability of getting exactly 6 tails?

## What is the probability of getting 6 consecutive tails?

Oct 16, 2017

The probability is $P = \frac{924}{4096} \approx 0.2256$.

#### Explanation:

Let $P$ be the probability of getting exactly $6$ tails, when a coin is tossed $12$ times.

Now let us consider the following:

1. probability of success from one toss be $\textcolor{red}{p}$.

2. probability of failure from one toss be $\textcolor{red}{q}$.

3. number of trials be $\textcolor{red}{n}$.

4. number of success be $\textcolor{red}{r}$.

5. number of failures is $\textcolor{red}{n - r}$.

Hence, the total probability of succeeding is represented by $\rightarrow$

$\textcolor{red}{P = n {C}_{r} {p}^{r} {q}^{r - x}}$.......(1).

Here,

$p = q = \frac{1}{2}$

$n = 12$ $\leftarrow$ Given.

$r = 6$ $\leftarrow$ Given.

$\therefore n - r = 6$

Now, substituting this into (1), we get

P=""_12C_6(1/2)^6(1/2)^6
color(white)P=(12!)/(6!(12-6)!)*1/2^12
$\textcolor{w h i t e}{P} = 924 \cdot \frac{1}{4096}$
$\textcolor{w h i t e}{P} \approx 0.2256$

Hope it Helps :)