In an experimental performance of a single throw of a pair of unbiased normal dice, let three events E₁, E₂ and E₃ are defined as follows: E₁ : getting prime numbered face on each dice. E₂ : getting the same number on each dice. E₃ : getting total on two dice equal to 4 . Which of the following is/are true?

Step-by-step solution

aligned & E₁= (2,2),(2,3),(3,2),(2,5),(5,2),(3,5),(5,3),(3,3),(5,5) & E₂= (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) & E₃= (1,3),(3,1),(2,2) aligned Now, P (E₁ )= 9 36 ; P (E₂ )= 6 36 ; P (E₃ )= 3 36 Clearly P (E₁ ), P (E₂ ), P (E₃ ) are in A.P. (1) is correct. P (E₁ E₂ )= 3 36 = 1 12 P (E₁ ) P (E₂ ) (2) is incorrect. Now, P (E₃ / E₁ )= P (E₃ E₁ ) P (E₁ ) = 1 9 (3) is incorrect. Also, aligned P (E₁+E₂ )+P (E₂-E₃ )= [P (E₁ )+P (E₂ )- . & .P (E₁ E₂ ) ] & + [P (E₂ )-P (E₂ E₃ ) ] = 9 36 + 12 36 - 3 36 - 1 36 = 17 36 & (4) is