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