Let two fair six - faced dice A and B be thrown simultaneously. If E 1 is the event that die A shows up four, E 2 is the event that die B shows up two and E 3 is the event that the sum of numbers on both dice is odd, then which of the following statement is NOT true ?

Step-by-step solution

E 1 → A show up 4 E 2 → B shows up 2 E 3 → Sum is odd (i.e., even + odd or odd + even) P E 1 = 6 6.6 = 1 6 P E 2 = 6 6.6 = 1 6 P E 3 = 3.3 6.6 + 3.3 6.6 = 2 4 = 1 2 P E 1 ∩ E 2 = 1 6.6 = P E 1 . P E 2 ⇒ E 1 a n d E 2 are independent P E 1 ∩ E 3 = 1.3 6.6 = P E 1 . P E 3 ⇒ E 1 a n d E 3 are independent P E 2 ∩ E 3 = 1.3 6.6 = 1 12 = P E 2 . P E 3 ⇒ E 2 a n d E 3 are independent P E 1 ∩ E 2 ∩ E 3 = 0 ≠ P ( E 1 ) × P ( E 2 ) × P ( E 3 )