A machine randomly generates one of the nine numbers 1, 2, 3, … , 9 with equal likelihood. What is the probability that when Tsuni uses this machine to generate four numbers their product is divisible by 4? Express your answer as a common fraction.

Guest Jul 20, 2022

#1**+1 **

Here's my best attempt at this one ....

There are C(9,4) = 126 possible sets

If we consider the sets whose product is NOT divisible by 4, we have the folowing cases

Case 1 - the set contains four of the following six integers .... { 1, 2 , 3, 5, 7 , 9 }

Total sets possible = C(6,4) = 15

Case 2 - the set contains four of the following six integers ....{1, 3 , 5, 6, 7 ,9 }

Total sets possible = C(6,4) = 15

Total sets whose product is divisible by 4 = 126 - 2(15) = 96

P ( that the set product is divisible by 4 ) = 96 / 126 = 16 / 21

[ I'd like someone to check this answer.....!!!! ]

CPhill Jul 21, 2022