Question

A die is thrown 6 times. If getting an odd number' is a success, then the probability 5 successes is :

• A. $\frac{3}{32}$
• B. $\frac{23}{5}$
• C. $\frac{32}{5}$
• D. $\frac{15}{32}$

Answer 1

The correct option is A $\frac{3}{32}$

Here, $n=6$

P(getting an odd number) = $P(1,3,5)=\frac{3}{6}=\frac{1}{2}$

$q=1-p=1-\frac{1}{2}=\frac{1}{2}$

P(5 successes) = $P\left(5\right)={6_C}_5\left(\frac{1}{2}\right)(\frac{1}{2}{)}^5=6\times (\frac{1}{2}{)}^6=6\times \frac{1}{64}=\frac{3}{32}$