A black and a red

Let B denote black colored die and R denote red colored die.

Then, the sample space for the given experiment will be:

(a) Let A be the event of ‘obtaining a sum greater than 9’ and B be the event of ‘getting a 5 on black die’.

Then, A = {(B4, R6), (B5, R5), (B5, R6), (B6, R4), (B6, R5), (B6, R6)}

And B = {(B5, R1), (B5, R2), (B5, R3), (B5, R4), (B5, R5), (B5, R6)}

⇒ A ∩ B = {(B5, R5), (B5, R6)}

So,

Now, we know that

By definition of conditional probability,

(b) Let A be the event of ‘obtaining a sum 8’ and B be the event of ‘getting a number less than 4 on red die’.

Then, A = {(B2, R6), (B3, R5), (B4, R4), (B5, R3), (B6, R2)}

And

⇒ A ∩ B = {(B5, R3), (B6, R2)}

So,

Now, we know that

By definition of conditional probability,