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# If six fair coins are tossed,what is the probability that at least one head appears?

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Feb 9, 2018

Probability of obtaining at least one head $= 0.9998756$

#### Explanation:

The coin is fair.
Probability of obtaining head $= 0.5$
Probability of obtaining tail $= 0.5$

Probability of obtaining at least one head $= 1 -$ Probability of obtaining no head

${P}_{x = 0} = {\text{_}}^{n} {C}_{x} \times {p}^{x} \times {q}^{n - x}$

${P}_{x = 0} = {\text{_}}^{6} {C}_{0} \times {0.5}^{0} \times {0.5}^{12 - 0}$

${P}_{x = 0} = 1 \times 1 \times {0.5}^{12 - 0} = 0.000244$

Probability of obtaining at least one head $= 1 - 0.000244 = 0.9998756$

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