An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is
Prob. of product being even = Favorable outcome/Total outcomes = (6n - 3n)/6n= 1- 1/2n
Total = 6n
Favor. = 6n - [no. formed by only 1,3,5] =6n - 3n
Here we need to find the probability that at least one time even number should come.
Product of Even and Odd = Even
Product of Even and Even =Even
Product of Odd and Odd =Odd
=1 - probability of coming only odds in "n" throws
The product will come even when at least one time an even number comes in n rolls.
P(even in 1 roll) =P(odd in 1 roll) =3/6 =1/2
P(atleast one time even in n rolls) = 1 - P(all times odd in n rolls) = 1 - 1/2n
Hence ,the correct answer is 1 - 1/2n
Option (e) None of the above ,is the ans.