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Popular >

a fair die is tossed five times what is th probability of obtaining an even number three times

Solution

a fair die is tossed five times what is th probability of obtaining an even number three times

Solution

\frac{5}{16}

Solution steps

Probability of an even number when a die is rolled:

\frac{1}{2}

For multiple independent trials

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

number of trials

n = 5

number of successes

x = 3

probability of success in any one trial

p = \frac{1}{2}

P (3) = 5 C 3 (\frac{1}{2})^{3} (1 - \frac{1}{2})^{5 - 3}

5 C 3 = 10

= 10 (\frac{1}{2})^{3} (\frac{1}{2})^{2}

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

= \frac{5}{16}

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