Two dice are thrown together and the total score is noted.

If two dice are thrown together, we have

n(S) = 36

Now, let’s consider:

E = A total of 4 = {(2, 2), (1, 3), (3, 1)} ⇒ n(E) = 3

F = A total of 9 or more

= {(3, 6), (6, 3), (5, 4), (4, 5), (5, 5), (4, 6), (6, 4), (5, 6), (6, 5), (6, 6)}

So, n(F) = 10

G = A total divisible by 5

= {(1, 4), (4, 1), (2, 3), (3, 2), (4, 6), (6, 4), (5, 5)}

So, n(G) = 7

It’s seen that (E ⋂ F) = Ø and (E ⋂ G) = Ø

And, (F ⋂ G) = {(4, 6), (6, 4), (5, 5)}

⇒ n(F ⋂ G) = 3 and (E ⋂ F⋂ G) = Ø

Hence, the probabilities if the events are