Question

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is.

• A. $\frac{63}{64}$
• B. $\frac{1}{2}$
• C. $\frac{127}{128}$
• D. $\frac{255}{256}$

Answer 1

Answer: (C)

$\frac{127}{128}$

$p=P\left(H\right)=\frac{1}{2}$, $q=P\left(T\right)=\frac{1}{2}$

$P$ (at least one head & one tail) = $P(1\le H\le 7$

$=1-[p\left(H\right)=0$ and $p\left(H\right)=8]$
$=1-[2\cdot (1/2{)}^8]$

$=1-[2\cdot \frac{1}{16\times 16}]$

$=1-\frac{1}{128}$

$=\frac{127}{128}$.