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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.

 Jul 20, 2022
 #1
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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.....!!!!  ]

 

cool cool cool

 Jul 21, 2022

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