Question

6 positive integers are taken at random and multiplied together. What is the probability that the product ends in an odd digit other than 5?

Answer 1

"Numbers = even (2,4,6,8), odd = (1,3,7,9)

odd*odd=odd

even*even=even

odd*even=even

=> all numbers should be odd=number of chance = 4^6

all possible chances = 9^6 probability=(4/9) ^ 6

Hence the prob for ending with 1, 3, 7, 9 is 1 - (6/10) = 4/10 = 2/5.

For 6 digits the prob is (2/5) ^ 6 = 64/15625

"