An ordinary dice is rolled for a certain number of times.

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 :

Accepted Answer

P(odd no. twice) = P(even no. thrice)

$$ \Rightarrow {}^n{C_2}{\left( {{1 \over 2}} \right)^n} = {}^n{C_3}{\left( {{1 \over 2}} \right)^n} \Rightarrow n = 5$$

Success is getting an odd number then P(odd successes) = P(1) + P(3) + P(5)

$$ = {}^5{C_1}{\left( {{1 \over 2}} \right)^5} + {}^5{C_3}{\left( {{1 \over 2}} \right)^5} + {}^5{C_5}{\left( {{1 \over 2}} \right)^5}$$

$$ = {{16} \over {{2^5}}} = {1 \over 2}$$

Solutions · 1