A fair coin is tossed 100 times. probability of getting tails an odd number of times is

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14.Probability

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A fair coin is tossed $100$ times. The probability of getting tails an odd number of times is

A

$\frac{1}{2}$

B

$\frac{1}{8}$

C

$\frac{3}{8}$

D

None of these

Solution

(a) The total number of cases are ${2^{100}}$

The number of favourable ways $= {}^{100}{C_1} + {}^{100}{C_3} + \,…….\, + {}^{100}{C_{99}} = {2^{100 – 1}} = {2^{99}}$

Hence required probability $ = \frac{{{2^{99}}}}{{{2^{100}}}} = \frac{1}{2}.$

Standard 11

Mathematics

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