If a fair coin is tossed 4 times, what is the probability that two heads and two tails will result?

If a fair coin is tossed 4 times, what is the probability that two heads and two tails will result? 

(A) $\dfrac{3}{8}$ 

(B) $\dfrac{1}{2}$ 

(C) $\dfrac{5}{8}$ 

(D) $\dfrac{3}{4}$ 

(GATE 2004) 

Answer: (A) $\dfrac{3}{8}$ 

Explanation: 

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

Here, the probability of 'success', $p = \dfrac{1}{2}$, and number of trials, $n = 4$. 

Therefore, by the binomial distribution, we get the required probability 

$= P(X = 2)$ 

$= {}^{4}\textrm{C}_{2}\left(\dfrac{1}{2}\right)^{2}\left(\dfrac{1}{2}\right)^{2}$ 

$= \dfrac{3}{8}$