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JEE Main202313 Apr 2023Morning ShiftMathematicsProbabilityActual

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the number of tosses of the coin, then the mean of X is

Options

  1. A38 16
  2. B15 16
  3. C21 16
  4. D81 64

Correct answer

C. 21 16

Step-by-step solution

It is given that P ( H ) = 3 P ( T ) ∴ P ( H ) = 3 4 , P ( T ) = 1 4 Since coin is tossed till either 1 H or 3 T occurs. So, process will end in the maximum of 3 throws. X i 1 2 3 P X i 3 4 1 4 · 3 4 1 4 × 1 4 × 1 4 + 1 4 × 1 4 × 3 4 Now we know that, Mean is given by ∑ i = 1 n X i P X i Mean = 1 × 3 4 + 2 × 3 16 + 3 × 1 16 = 21 16 Hence, this is the correct option.

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