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From a pack of 52 cards, we draw one by one, without replacement. If \(f(n)\) is the probability that an Ace will appear at the \(n^{\text{th}}\) turn, then

Question and options

From a pack of 52 cards, we draw one by one, without replacement. If f(n)f(n) is the probability that an Ace will appear at the nthn^{\text{th}} turn, then
  1. f(2)=113>f(3)f(2) = \frac{1}{13} > f(3)
  2. 113>f(2)>f(3)\frac{1}{13} > f(2) > f(3)
  3. f(3)>f(2)=113f(3) > f(2) = \frac{1}{13}
  4. f(2)=f(3)=113f(2) = f(3) = \frac{1}{13}

Answer and explanation

Correct answer: D - \(f(2) = f(3) = \frac{1}{13}\)
By symmetry each position is equally likely to hold any card, so P(Ace at nth draw) = 4/52 = 1/13 for every n; f(2) = f(3) = 1/13.

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  • IPMAT Indore

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