# Eight coins are tossed together.The probability of getting exactly 3 heads is Option 1) $\frac{1}{256}$ Option 2) $\frac{7}{32}$ Option 3) $\frac{5}{32}$ Option 4) $\frac{3}{32}$

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as

$P\left ( E \right )=\frac{n\left ( E \right )}{n\left ( S \right )}$

$P\left ( E \right )\leq 1$

$P(E)=\lim_{n\rightarrow\infty}\left(\frac{r}{n} \right )$

- wherein

Where n repeated experiment and E occurs r times.

Probability of getting exactly 2 heads is

$8_{C}_{}_{3}.$$(\frac{1}{2})^{8}\Rightarrow \frac{81}{3151}\times \frac{1}{256}$

$\frac{8\times 7\times 6}{6}\times \frac{1}{256}$

$=\frac{7}{32}$

Option 1)

$\frac{1}{256}$

This option is incorrect

Option 2)

$\frac{7}{32}$

This option is correct

Option 3)

$\frac{5}{32}$

This option is incorrect

Option 4)

$\frac{3}{32}$

This option is incorrect

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