Four positive integers are taken at random and are multiplied together. Then the probability that the product ends in an odd digit than 5 is

Options

A. `(3)/(5)`
B. `(609)/(625)`
C. `(16)/(625)`
D. `(2)/(5)`

Answer

C

Explanation

We want that the product ends in an odd digit other than 5. This means that the digit at units place in each number is one of the digits 1,3,7,9.
`therefore` Probability of selecting such a digit in a number at unit's is `=(4)/(10)`
Hence, required probability `=((4)/(10))^(4)=(16)/(625)=(1)/(2^(2n+1)). 2^(2n)=(1)/(2)`