A black and a red dice are rolled.

(a) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.


(b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

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,





13