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If \(P\) and \(Q\) each toss three coins. The probability that both gets same number of heads, is
Options:
Solution:
1368 Upvotes
Verified Answer
The correct answer is:
\(\frac{5}{16}\)
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.
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.
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