Two dice are thrown together and the total score is noted. The events E, F and G are ‘a total of 4’, ‘a total of 9 or more’, and ‘a total divisible by 5’, respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are independent.

Given that two dice are drawn together i.e. n(S)= 36

Where S is sample space

Also given that

E = a of total 4

∴E = {(2,2), (3,1), (1,3)}

∴n(E) = 3

And F= a total of 9 or more

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

∴n(F)=10

And,

G = a total divisible by 5

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

∴ n(G) = 7

Here, (E Ո F) = φ AND (E Ո G) = φ

Also, (F Ո G) = {(4,6), (6,4), (5,5)}

n (F Ո G) = 3 and (E Ո F Ո G) = φ

And,

So,

P (F Ո G) ≠ P(F). P(G)

hence, there is no pair which is independent