Mathcount probability problem

[westin]

Hi,

This is a mathcount math contest problem. The answer is 2096/6561.

Divisibility rule of 14 is the number is divisible by 2 and by 7. I know hat 6561 is 9^4.

Besides that I don't know how to proceed, can someone give my some hints.

thanks!

 

[Steven G]

...therefore the problem is asking if you pick 4 numbers from 1,2,3,4,5,6,7,8,9 then what is the probability that you pick includes 2 and 7.
Keep in mind that the machine can pick the same number up to 4 times.

 

[Dr.Peterson]

This may be a good problem for which to use complements.

Can you find the probability that the product of the four numbers is NOT divisible by 14? That means either no 7 is chosen, or no even number is chosen ...

 

[Harry_the_cat]

...therefore the problem is asking if you pick 4 numbers from 1,2,3,4,5,6,7,8,9 then what is the probability that you pick includes 2 (OR ANY EVEN NUMBER) and 7.
Keep in mind that the machine can pick the same number up to 4 times.

see bold

 

[BigBeachBanana]

Hi,

This is a mathcount math contest problem. The answer is 2096/6561.

Divisibility rule of 14 is the number is divisible by 2 and by 7. I know hat 6561 is 9^4.

Besides that I don't know how to proceed, can someone give my some hints.

thanks!

Phrased differently: What's the probability that you pick AT LEAST ONE 7 and AT LEAST an even number out of 4 times?

 

[Steven G]

...therefore the problem is asking if you pick 4 numbers from 1,2,3,4,5,6,7,8,9 then what is the probability that you pick includes 2 (OR ANY EVEN NUMBER) and 7.
Keep in mind that the machine can pick the same number up to 4 times.

see bold

OUCH!