A person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score X is obserbed, then the range of X is

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{0, 3, 6}

{–3, 0, 3, 6}

{–3, 0, 3}

{–3, 3, 6}

answer is C.

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Detailed Solution

3 Coins are tossed. So, we have 4 possible out comes.

$1) 3 T, 0 H \Rightarrow Score = - 3 2) 2 T, 1 H \Rightarrow Score = - 2 + 2 = 0 3) 1 T, 2 H \Rightarrow Score = - 1 + 4 = 3 4) 0 T, 3 H \Rightarrow Score = 0 + 6 = 6$

Hence range of $x = \{- 3, 0, 3, 6\}$

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