Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.

The sample space of the given experiment is:

Let E be the event that ‘the sum of numbers on the dice is 4’ and F be the event that ‘the two numbers appearing on throwing the two dice are different’.

⇒ E = {(1, 3), (2, 2), (3, 1)}

And

⇒ E ∩ F = {(1, 3), (3, 1)}

……….(i)

Now, we know that

By definition of conditional probability,

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