E₁ and E₂ are two independent events of a random experiment such that P (E₁ )= 1 2 and P (E₁ E₂ )= 2 3 . Then match the items of List-I with the items of List-II. The correct match is

Step-by-step solution

P ( E ₁ )= 1 2 , P ( E ₁ E ₂ )= 2 3 Since, E₁ and E₂ are independent events P (E₁ E₂ )=P (E₁ ) P (E₂ ) P (E₁ E₂ )= 1 2 P (E₂ ) ...(i) aligned & Also, P (E₁ E₂ )=P (E₁ )+P (E₂ )-P (E₁ E₂ ) & 2 3 = 1 2 +P (E₂ )- 1 2 P (E₂ ) [Using(i)] & 1 6 = 1 2 P (E₂ ) 1 3 =P (E₂ ) & So, P (E₁ E₂ )= 1 2 1 3 = 1 6 & P ( E₁ E₂ )= P (E₁ E₂ ) P (E₂ ) = 1 6 3= 1 2 & P ( E ₂ E₁ )= P ( E ₂ E₁ ) P (E₁ ) = P (E₁ )-P (E₁ E₂ ) P (E₁ ) = 1 2 - 1 6 1 2 = 2 3 & P ( E ₁ E ₂ )=P ( E₁ E₂ )=1-P (E₁ E₂ )=1- 1 6 = 5 6 aligned