Multiple choice

A coin is tossed three times. If $X$ denotes the absolute difference between the number of heads and the number of tails then $P(X=1)=$

  1. $\cfrac { 1 }{ 2 } $
  2. $\cfrac { 2 }{ 3 } $
  3. $\cfrac { 1 }{ 6 } $
  4. $\cfrac { 3 }{ 4 } $
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D Correct answer
Explanation

Possible outcomes for 3 tosses: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. X is the absolute difference between heads and tails. For 3 tosses, the counts are (3,0) or (0,3) where X=3, and (2,1) or (1,2) where X=1. There are 3 outcomes with 2 heads (HHT, HTH, THH) and 3 with 1 head (HTT, THT, TTH). Total outcomes = 8. P(X=1) = 6/8 = 3/4.

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