If \(P\) and \(Q\) each toss three coins. The probability that both gets same number of heads, is
If \(P\) and \(Q\) each toss three coins. The probability that both gets same number of heads, is
\(\frac{3}{8}\)
\(\frac{1}{9}\)
\(\frac{3}{16}\)
\(\frac{5}{16}\)
Solution
Let \(p\) and \(q\) represents the probability of getting head and tail respectively on tossing a coin.
So, \(p=q=\frac{1}{2}\)
\(\begin{aligned}
\text { So, required probability } & =\sum_{r=0}^3\left[3_{\mathrm{C}_r}\left(\frac{1}{2}\right)^3\right]^2 \\
& =\left(\frac{1}{2}\right)^6\left[1^2+3^2+3^2+1^2\right] \\
& =\frac{20}{64}=\frac{5}{16}
\end{aligned}\)
Hence, option (d) is correct.