It is given that E1 and E2 are the two events such that P (E1) = 1/4, P (E2) = 1/3 and P (E1 U E2) = 1/2
We know that
P (E1 ∩ E2) = P (E1) + P (E2) – P (E1 U E2)
By substituting the values
= 1/4 + 1/3 – 1/2
= 1/12 …….. (1)
Condition: Two events are independent
P (E1 ∩ E2) = P (E1) × P (E2)
By substituting the values
= 1/4 × 1/3
= 1/12 ……. (2)
Here both the equations are same
So E1 and E2 are independent events
Therefore, it is proved.