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COMEDK202510 May 2025Evening ShiftMathematicsProbabilityActual

A bag contains (n+1) coins. It is known that one of these coins has a head on both sides, whereas the other coins are fair. One of these coins is selected at random and tossed. If the probability that the toss results in heads is 7 12 , then the value of n is

Options

  1. A4
  2. B5
  3. C2
  4. D3

Correct answer

B. 5

Step-by-step solution

Let E be the event that the selected coin shows heads. Let C₁ be the event that the two-headed coin is selected, and C₂ be the event that a fair coin is selected. The probability of selecting the two-headed coin is P(C₁) = 1 n+1 . The probability of selecting a fair coin is P(C₂) = n n+1 . The probability of getting heads given the two-headed coin is P(E|C₁) = 1 . The probability of getting heads given a fair coin is P(E|C₂) = 1 2 . Using the law of total probability, P(E) = P(E|C₁)P(C₁) + P(E|C₂)P(C₂) . Substituti

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