Each of the persons A and B
Question:

Each of the persons $\mathrm{A}$ and $\mathrm{B}$ independently tosses three fair coins. The probability that both of them get the same number of heads is :

1. $\frac{1}{8}$

2. $\frac{5}{8}$

3. $\frac{5}{16}$

4. 1

Correct Option: 3,

Solution:

T T T $\quad\left(\frac{1}{2}\right)^{3}\left(\frac{1}{2}\right)^{3}=\frac{1}{64}$

H T T $\quad\left(\frac{3}{8}\right)\left(\frac{3}{8}\right)=\frac{9}{64}$

H H T $\quad\left(\frac{3}{8}\right)\left(\frac{3}{8}\right)=\frac{9}{64}$
$\mathrm{HHH} \quad\left(\frac{1}{8}\right)\left(\frac{1}{8}\right)=\frac{1}{64}$
Total probability $=\frac{5}{16} .$