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MHT CET202411 May 2024Evening ShiftMathematicsProbabilityActual

One hundred identical coins, each with probability p , of showing up heads are tossed once. If 0 p 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is

Options

  1. A1 2
  2. B49 101
  3. C50 101
  4. D51 101

Correct answer

D. 51 101

Step-by-step solution

aligned & We have ¹⁰⁰ C ₅₀ p ⁵⁰(1- p )⁵⁰= ¹⁰⁰ C ₅₁ p ⁵¹(1- p )⁴⁹ & 1- p p = 100! 51!49! 50!.50! 100! = 50 51 & 51-51 p =50 p & p = 51 101 aligned

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