Question

If E₁ and E₂ are two events such that P(E₁) = 1/4;  P(E₂) = 1/2; P(E₁/E₂) = 1/4,  then choose the correct options.

(i) E₁ and E₂ are independent 

(ii) E₁ and E₂ are exhaustive 

(iii) E₁ and E₂ are mutually exclusive 

(iv) E₁ & E₂ are dependent

Also find P(bar E₁/E₂) and (E₂/E₁)

Answer 1

=> E₁ and E₂ are independent of each other 

Also since P(E₁ ∪ E₂) = P(E₁) + P(E₂) – P(E₁) . P(E₂) ≠ 1 

Hence events are not exhaustive. Independent events can’t be mutually exclusive. 

Hence only (i) is correct Further since E₁ & E₂ are independent;