Question

A single coin is tossed $5$ times. What is the probability of getting at least one head?

• A. $\frac{27}{32}$
• B. $\frac{3}{32}$
• C. $\frac{1}{32}$
• D. $\frac{31}{32}$

Answer 1

The correct option is D $\frac{31}{32}$

Let us assume a coin is fair and 2-sided. A coin usually flips heads or tails. Then to flip heads or tails equals $\frac{1}{2}$. Consider flip a coin 5 times. Since a coin flip has two outcomes, then a coin flip 5 times has $2^5=32$ outcomes.

We may show the outcomes, e.g. use sample space S. Then

(1)$S=(H,H,H,H,H),(H,H,H,H,T),\dots ,(T,H,H,H,H),(T,T,T,T,T)$

It must follow $|S|=32$. A helpful way to see may be $S={H,T}^5=H,Tx\dots xH,T.$ If you see the complement of at least 1 tails means 0 tails or 5 heads, then we must surely see 1 outcome, e.g. all heads. Then it must follow at least one tails has $31outcomes,e.g.32–1=31$.

To find or compute the probability, then #favorable/#possible in outcomes. It means 31/32, e.g. or $P\left(E\right)=1–\frac{1}{32}=\frac{31}{32}.$