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If a fair coin is tossed 6 times, what is the probability, to the nearest thousandth, of getting exactly 3 tails?

Solution

If a fair coin is tossed 6 times, what is the probability, to the nearest thousandth, of getting exactly 3 tails?

Solution

\frac{5}{16}

Solution steps

Probability of a tail 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 = 3

probability of success in any one trial

p = \frac{1}{2}

P (3) = 6 C 3 (\frac{1}{2})^{3} (1 - \frac{1}{2})^{6 - 3}

6 C 3 = 20

= 20 (\frac{1}{2})^{3} (\frac{1}{2})^{3}

20 (\frac{1}{2})^{3} (\frac{1}{2})^{3} = \frac{5}{16}

= \frac{5}{16}

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