Question

Let two fair six-faced dice A and B be thrown simultaneously. If E₁ is the event that dice A shows up four, E₂ is the event that dice B shows up two and E₃ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true? 

(A) E₁, E₂ and E₃ are independent. 

(B) E₁ and E₂ are independent. 

(C) E₂ and E₃ are independent. 

(D) E₁ and E₃ are independent.

Answer 1

Answer is (A) E₁, E₂ and E₃ are independent.

We have E₁ → Dice A shows 4

E₂ → Dice B shows 2

E₃ → Sum odd (No. on A to be odd + No. on B to be even or No. on B to be odd + No. on A to be even)

Therefore,

Thus, the events are independent.