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  • Help me please, Eight coins are tossed together.The probability of getting exactly 3 heads is

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}

 

Answers (1)

best_answer

 

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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