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

Solution:
Assuming: B denote black coloured die and R denote red coloured die.

Therefore, the sample space for the specified experiment will be as follows:

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

Then,

And

So,

Now, we know that by definition of conditional probability,

Now by substituting the values we get

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

We have sample space of common event,

The probability of the event,

Now, we know that

By relation of conditional probability,

Now by substituting the values we get