Question

An unbiased coin is tossed to get $2$ points for turning up a head and one point for the tail. If three unbiased coins are tossed simultaneously, then the prob. of getting a total of odd no. of points is

• A. $1/2$
• B. $1/4$
• C. $1/8$
• D. $3/8$

Answer 1

Answer: (A)

$1/2$

$2$ points for Head and $1$ point for Tail
Cases of getting a total of odd no. of points is:
Sum of three number will be odd when all three are odd or one is odd and two are even.
Case 1: $OOO=$ when all are tails $=TTT=1$ case
Probability when all are tails $=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{8}$
Case 2: $OEE=$ When one is tails and two are head $=THH=3$ cases

Probability when one is tails and two are head$=3\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{3}{8}$

Probability of getting a total of odd no. of points is$=\left(\frac{1}{8}\right)+\left(\frac{3}{8}\right)=\frac{1}{2}$