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

解

I f a f ai r co in i s t osse d 6 t im es, w ha t i s t h e p ro babi l i t y, t o t h e n e a res t t h o u s an d t h, o f g e tt in g e x a c tl y 3 t ai l s ?

\frac{5}{16}

十進法表記

0.3125

解答ステップ

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}