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.

Question

Philoid · Accepted Answer

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