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:

C-I ‘0’ Head

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

C-II ‘1’ head

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

C-III ‘2’ Head

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

C-IV’3′ Heads

$\mathrm{HHH} \quad\left(\frac{1}{8}\right)\left(\frac{1}{8}\right)=\frac{1}{64}$

Total probability $=\frac{5}{16} .$

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