Question

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :

• A. $\frac{1}{32}$
• B. $\frac{5}{16}$
• C. $\frac{3}{16}$
• D. $\frac{1}{2}$

Answer 1

Answer: (D)

${ }^{ n } C _{2}\left(\frac{1}{2}\right)^{ n }={ }^{ n } C _{3}\left(\frac{1}{2}\right)^{ n } $
$\Rightarrow { }^{ n } C _{2}={ }^{ n } C _{3}$
$\Rightarrow n =5$
Probability of getting an odd number for odd number of times is
${ }^{5} C _{1}\left(\frac{1}{2}\right)^{5}+{ }^{5} C _{3}\left(\frac{1}{2}\right)^{5}+{ }^{5} C _{5}\left(\frac{1}{2}\right)^{5}=\frac{1}{2^{5}}(5+10+1)$
$=\frac{1}{2}$