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
So,
P (F Ո G) ≠ P(F). P(G)
Hence, there is no pair which is independent
