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 :
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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