Let X denotes the number of heads in a single toss of 4 fair coins,

Match List I with List II.

Choose the correct answer from the options given below:

A-IV, B-I, C-II, D-III

The correct answer is Option (1) → A-IV, B-I, C-II, D-III

$X \sim \text{Binomial}(n=4,\; p=\frac{1}{2})$

$\text{(A)}\; P(X=3)=\frac{4!}{3!1!}\left(\frac{1}{2}\right)^4=\frac{4}{16}=0.25 \Rightarrow \text{(IV)}$

$\text{(B)}\; E(X)=np=4\cdot\frac{1}{2}=2 \Rightarrow \text{(I)}$

$\text{(C)}\; E(X^2)=npq+(np)^2=4\cdot\frac{1}{2}\cdot\frac{1}{2}+2^2=1+4=5 \Rightarrow \text{(II)}$

$\text{(D)}\; P(1\le X \le3)=P(2)+P(3)=\frac{6}{16}+\frac{4}{16}=\frac{10}{16}=0.625\approx0.63 \Rightarrow \text{(III)}$

A–IV,\; B–I,\; C–II,\; D–III