Question

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 observed, then the range of $X$ is

• A. $0,3,6$
• B. $-3,0,3$
• C. $-3,0,3,6$
• D. $-3,3,6$

Answer 1

The correct option is C $-3,0,3,6$

$3$ coins are tossed . There can be $4$ possible outcomes
$1.3T,0H$. Score $=-3$
$2.2T,1H$. Score $=-2+2=0$
$3.1T,2H$. Score $=-1+4=3$
$4.0T,3H$. Score $=0+6=6$
Hence, the range of $X$ is $\{-3,0,3,6\}$