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JEE Main 2017 · Mathematics · Probability · easy

When an unbiased coin is flipped five times, the chance that heads shows up in exactly three flips is

Single correct option

When an unbiased coin is flipped five times, the chance that heads shows up in exactly three flips is
  1. A. 316\dfrac{3}{16}
  2. B. 516\dfrac{5}{16}
  3. C. 532\dfrac{5}{32}
  4. D. 12\dfrac{1}{2}
Show answer and solution

Answer: (B) 516\dfrac{5}{16}

The number of heads follows a binomial distribution with n=5n=5 and p=12p=\tfrac12. So P(X=3)=(53)(12)3(12)2=1032=516P(X=3)=\binom53\left(\tfrac12\right)^3\left(\tfrac12\right)^2=\dfrac{10}{32}=\dfrac{5}{16}. The option 5/325/32 forgets the binomial coefficient of 10 and uses only 5.
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Original question written in the JEE Main 2017 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake