Question

A certain machine randomly generates an integer between 1 and 9, inclusive. The machine generates n numbers, and all the outputs are multiplied together. What is the probability that the resulting product is divisible by 10?

Answer 1

n-numbers are one So n must be ( Probability of getting any digit is į ie. pag Generated multiplied together The product will divisible by to if there is at least '5', and one of '2','4', 6,8 greater of equal to 2. Probability that there is no 5 in the n numbers is (& Probability that there is at least one's' is 1-(8) Probability of being attend the '2' is to pray in '4' is Ire (1-2) อ) n 16' is I- comun igs is () is

Probability of being at least of one of zegt, = ar 'go, is, P (2) UP (4) UAP (6) UP (8) P(2) + P(4) + P (6) + P18) P(29:P(49 - P(2).P16) P(21.818) - P(49.8169 ~P(4):P(8) - P169.P18) & P (29. P (4) .P (6) + P (2), P (4) .P (8) +P (2).P(6) .P (8) of P (4) .P (6) .P(8) P(2) .P(4) .P(6) .P(8) 3 's and one even tigit qe (1-(8)") - 671-68574747-477 - {1-49" 29 Probability of being at least one's' and PCG x{PC2) U PC49 UPCEJ U P (8)? 4 (1-699-670-4890293 24-455939 - pery This is the probability that the product will P +4 divisible by too