Probability question - hypergeometric distribution?

Hi,



I have never quite worked this type of probability question out, so would like some help please.



Imagine this scenario:

There are 4 people sat around a table, A, B, C and D.

A is sitting opposite C, B is sitting opposite D.

There is a bag with 16 balls numbered 1-16.

The balls are randomly drawn so that each person has 4 balls.



Imagine you are A.

And the balls you have are 1,4,5,9.



Now you want to work out what is the probability that C has a ball that is higher than your highest ball i.e. you want to work out whether C has AT LEAST one of 10,11,12,13,14,15, or 16.



Now the way I look at it is that the:

probability of C having ball 10 is 1/3

probability of C having ball 11 is 1/3

probability of C having ball 12 is 1/3

probability of C having ball 13 is 1/3

probability of C having ball 14 is 1/3

probability of C having ball 15 is 1/3

probability of C having ball 16 is 1/3



But I just don't know what to do next. Any assistance would be appreciated.



Thanks.