A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, ‘the number is even,’ and B be the event, ‘the number is red’. Are A and B independent?

Given: A die is given.

The sample space for the dice will be:

S = {1, 2, 3, 4, 5, 6}

Let A be the event, the number is even:

⇒ A = {2, 4, 6}

Now, Let B be the event, the number is red:

⇒ B = {1, 2, 3}

⇒ P(B) =

As, A ∩ B = {2}

⇒ P(A ∩ B) = ..(1)

And P(A) . P(B) = ..(2)

From (1) and (2) P (A ∩ B) ≠ P(A) . P(B)

Therefore, A and B are not independent events.

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