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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
100 identical coins, each with probability $p$ of showing heads, are tossed.
If $0 < p < 1$ and the probability of showing heads on 50 coins is equal to that of 51 coins, then the value of $p$ is:
Solution
$\binom{100}{50}p^{50}(1-p)^{50} = \binom{100}{51}p^{51}(1-p)^{49}$ $\Rightarrow \dfrac{\binom{100}{50}}{\binom{100}{51}} \cdot \dfrac{1-p}{p} = 1$ $\dfrac{\binom{100}{50}}{\binom{100}{51}} = \dfrac{51}{50}$ $\Rightarrow \dfrac{1-p}{p} = \dfrac{50}{51}$ $\Rightarrow p = \dfrac{51}{101}$Online Test Series, Information About Examination,
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