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JEE Main202226 Jun 2022Morning ShiftMathematicsProbabilityActual

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is

Options

  1. A46 6 4
  2. B275 6 5
  3. C41 5 5
  4. D36 5 4

Correct answer

A. 46 6 4

Step-by-step solution

P 4   heads = P 5   heads 5 C 4 p 4 q =   5 C 5 p 5 ⇒ p = 5 q           . . . i Also, p + q = 1 ⇒ q = 1 6 , p = 5 6 (from i ) So, P (at most 2 heads) = P x = 0 + P x = 1 + P x = 2 = q 5 + 5 C 1 p q 4 + 5 C 2 p 2 q 3 = 1 6 5 + 5 5 6 1 6 4 + 10 5 6 2 1 6 3 = 46 6 4

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