Q51 / 90 · JEE Main 2017 (08 Apr Online) · Mathematics

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

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

Solution

Probability of at least one head and at least one tail can be calculated as,

$= 1 -{P (A l l H e a d) + P (A l l T a i l)}$

$= 1 - \{\frac{1}{2^{8}} + \frac{1}{2^{8}}\}$

$= 1 - \frac{1}{2^{7}}$

$= 1 - \frac{1}{128} = \frac{127}{128}$

Hence, the correct answer is option: 'A'.

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