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Popular Word Problems >

3 coins is tossed 7 times. What is the probability 3 heads?

Solution

3 co in s i s t osse d 7 t im es . Wha t i s t h e p ro babi l i t y 3 h e a d s ?

Solution

\frac{35}{128}

+1

Decimal

0.2734375

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 = 7

number of successes

x = 3

probability of success in any one trial

p = \frac{1}{2}

P (3) = 7 C 3 (\frac{1}{2})^{3} (1 - \frac{1}{2})^{7 - 3}

7 C 3 = 35

= 35 (\frac{1}{2})^{3} (\frac{1}{2})^{4}

35 (\frac{1}{2})^{3} (\frac{1}{2})^{4} = \frac{35}{128}

= \frac{35}{128}

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