An unbiased coin is tossed eight times. The probability of o... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

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

A

$\frac{255}{256}$

B

$\frac{127}{128}$

C

$\frac{63}{64}$

D

$\frac{1}{2}$

Answer

$\frac{127}{128}$

Explanation

Solution

1 - $\int$ P(All Head) + P(AllTail)
$1 - \left\\{\frac{1}{2^{8}}+\frac{1}{2^{8}}\right\\}$
$= 1-\frac{1}{2^{7}}$
$= 1-\frac{1}{128} = \frac{127}{128}$