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. (a) find the probability that the first number is 4, given that the sum is 9. (b) find the probability that the first number is 3, given that the sum is 8.

(a)

The probability is :  1/2

(b)

The probability is :  1/2

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: