<h2>
Answer:</h2>
(a)
The probability is :  1/2
(b)
The probability is :  1/2
<h2>
Step-by-step explanation:</h2>
The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement.
The total combinations that are possible are:
(1,2)   (1,3)    (1,4)    (1,5)
(2,1)   (2,3)   (2,4)   (2,5)
(3,1)   (3,2)   (3,4)   (3,5)
(4,1)   (4,2)   (4,3)   (4,5)
(5,1)   (5,2)   (5,3)   (5,4)
i.e. the total outcomes are : 20
(a)
Let A denote the event that the first number is 4.
and B denote the event that the sum is: 9.
Let P denote the probability of an event.
We are asked to find: 
                P(A|B)
We know that it could be calculated by using the formula:

Hence, based on the data we have:

( Since, out of a total of 20 outcomes there is just one outcome which comes in A∩B and it is:  (4,5) )
and

( since, there are just two outcomes such that the sum is: 9
(4,5) and (5,4) )
Hence, we have:

(b)
Let A denote the event that the first number is 3.
and B denote the event that the sum is: 8.
Let P denote the probability of an event.
We are asked to find: 
                P(A|B)
Hence, based on the data we have:

( since, the only outcome out of 20 outcomes is:  (3,5) )
and

( since, there are just two outcomes such that the sum is: 8
(3,5) and (5,3) )
Hence, we have:
