A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?

A coin is tossed 4 times. What is the probability of getting heads exactly 3 times? 

(A) $\dfrac{1}{4}$ 

(B) $\dfrac{3}{8}$ 

(C) $\dfrac{1}{2}$ 

(D) $\dfrac{3}{4}$ 

Answer: (A) $\dfrac{1}{4}$ 

Explanation: 

Let $X$ be a random variable that denotes the number of heads. 

Here, $X$ follows the binomial distribution with the parameters $p = \dfrac{1}{2}$ and $n = 4$. 

Hence, $P(X = r) = ^nC_r \times p^r \times (1 - p)^{n - r}$, where $r = 1, \ldots, n$. 

Therefore, the required probability is 

$P(X = 3) = ^4C_3 \times (\dfrac{1}{2})^3 \times (1 - \dfrac{1}{2})^{4 - 3}$ 

$= 4 \times \dfrac{1}{8} \times \dfrac{1}{2}$ 

$= \dfrac{1}{4}$