A game consists of tossing a coin 3 times and noting its outcome. A boy wins the game if all tosses give the…
A game consists of tossing a coin 3 times and noting its outcome. A boy wins the game if all tosses give the same outcome (i.e three heads or three tails) and loses the game otherwise. The probability that the boy loses the game is
$\frac{3}{4}$
$\frac{1}{4}$
$\frac{2}{3}$
$\frac{1}{3}$
Solution
Number of sample space $=2 \times 2 \times 2=8$
Now, favourable outcome $=\left\{\begin{array}{l}\text { HHT, HTH, HTT } \\ \text { THH, THT, TTH }\end{array}\right\}$
So required probability $=\frac{6}{8}=\frac{3}{4}$