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
${}^5{C}_1{\left(\frac{1}{2}\right)}^5+{}^5{C}_3{\left(\frac{1}{2}\right)}^5+{}^5{C}_5{\left(\frac{1}{2}\right)}^5=\frac{1}{2^5}(5+10+1)$
$=\frac{1}{2}$