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If a fair coin is tossed 6 times, what is the probability, to the nearest thousandth, of getting exactly 4 heads?

Solution

If a fair coin is tossed 6 times, what is the probability, to the nearest thousandth, of getting exactly 4 heads?

Solution

\frac{15}{64}

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 = 6

number of successes

x = 4

probability of success in any one trial

p = \frac{1}{2}

P (4) = 6 C 4 (\frac{1}{2})^{4} (1 - \frac{1}{2})^{6 - 4}

6 C 4 = 15

= 15 (\frac{1}{2})^{4} (\frac{1}{2})^{2}

15 (\frac{1}{2})^{4} (\frac{1}{2})^{2} = \frac{15}{64}

= \frac{15}{64}

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