Question

A pair of fair dice is rolled. Let E denote the event that the number landing uppermost on the first die is a 3, and let F denote the event that the sum of the numbers landing uppermost is 7. Determine whether E and F are independent events.

For E and F to be independent, doesn't P(E l E) have to be equal to P(F)?
I know for F, there are 6 ways to sum up 7 (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

Answer 1

Sorry, I meant doesn't P (F l E) have to be equal to P (F)? Or vice versa ( P(E l F) be equal to P(E)?

Answer 2

If the first die is 3, then to sum as 7, the second die has to be 4. Is that independence?