Question

A fair coin is tossed $3$ times. A person receives $Rs.X^2$ if he gets $X$ number of heads in all. Find his expected gain.

Answer 1

A fair coin is based $3$ times

we have $2^3$ possible out canel

i.e., $8$

$1.HHH$

$2.HHT$

$3.HTH$

$4.HTT$

$5.THH$

$6.THT$

$7.TTH$

$8.TTT$

$\therefore$ no. of heads $=12$ heads from $3$ coin tosses

$\therefore x=12$

$x^2=14.4$

$\therefore$ expected gain is $144Rs$