Prove or give counterexamples to the following

Step 1 of 3

a) We have to give the example for if E is independent of F and E is independent of G then E is independent of

Let’s take the example of rolling 2 dice

Let E be the event that sum of 7

Let F be the event that first die does not land on 4

Let G be the event that second die does not land on 3

Now

                              = 

                              =5/35

Now

                   =6/36

                   =?

Then

Hence E is not independent of

Hence the given statement is not true