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What is the probability of getting 6 heads when you flip a coin nine times?

Solution

What is the probability of getting 6 heads when you flip a coin nine times?

Solution

\frac{21}{128}

Solution steps

Probability of a head when a coin is thrown:

\frac{1}{2}

For multiple independent trials

P (x) = n C x \cdot p^{x} \cdot (1 - p)^{n - x}

number of trials

n = 9

number of successes

x = 6

probability of success in any one trial

p = \frac{1}{2}

P (6) = 9 C 6 (\frac{1}{2})^{6} (1 - \frac{1}{2})^{9 - 6}

9 C 6 = 84

= 84 (\frac{1}{2})^{6} (\frac{1}{2})^{3}

84 (\frac{1}{2})^{6} (\frac{1}{2})^{3} = \frac{21}{128}

= \frac{21}{128}

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