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 statements is not true?

Question

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 statements is not true?, E 1 and E 3 are independent, E 1 , E 2 and E 3 are independent, E 1 and E 2 are independent, E 2 and E 3 are independent

MARKS App · Accepted Answer

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 & E 2 are independent P E 1 ∩ E 3 = 1.3 6.6 = P E 1 . P E 3 ⇒ E 1 & E 3 are independent P E 2 ∩ E 3 = 1.3 6.6 = 1 12 = P E 2 . P E 3 ⇒ E 2 & E 3 are independent P E 1 ∩ E 2 ∩ E 3 = 0 ≠ P ( E 1 ) × P ( E 2 ) × P ( E 3 )

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