Q. 104.1( 62 Votes )

A black and a red

Answer :

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,





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