Question

Five coins are tossed simultaneously. Find the probability of event that at least one head turns up. (Assume that wins are fair).

Answer 1

Let $A$ be the event that ‘at lest one head turns up.

since each coin turns up on either a head or a tail.

Hence, the sample space consists of $2^5=32$ outcomes.

Each outcome having a probability of occurrence as $\frac{1}{32}$ .

Then $A^c$ is the event that ‘No head turns up’.

Thus $A^c$ consists of only one outcome,

Hence $P\left(A^c\right)=\frac{1}{32}$

$\Rightarrow P\left(A\right)=1-\frac{1}{32}=\frac{32-1}{32}=\frac{31}{32}$