Question

Nayan tosses a coin thrice. Find the probability of getting a) exactly $2$ heads and b) at most $2$ tails

Answer 1

When the coin is tossed trice, the possible outcomes are $HHH,HHT,HTH,HTT,THH,THT,TTH,TTT$.
Total number of possible outcomes $=8$.
a) Let $A$ be the event of getting exactly $2$ heads. Then, the favourable outcomes are $HHT,HTH,THH$, which is equal to $3$. That is, the number of favourable outcomes $=3$.
Therefore $P\left(A\right)=\frac{3}{8}$.
b) Let $B$ be the event of getting at most $2$ tails.
Then $B=$ the event of getting $1$ or $2$ tails.
The favourable outcomes are $HHH,HHT,HTH,HTT,THH,THT,TTH$.
The number of favourable outcomes $=7$.
Therefore $P\left(B\right)=\frac{7}{8}$.