Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If \(P\) and \(Q\) each toss three coins. The probability that both gets same number of heads, is
MathematicsProbabilityAP EAMCETAP EAMCET 2020 (18 Sep Shift 2)
Options:
  • A \(\frac{3}{8}\)
  • B \(\frac{1}{9}\)
  • C \(\frac{3}{16}\)
  • D \(\frac{5}{16}\)
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.

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.