Question

There are two boxes, each containing slips numbered 1 to 5. One slip is drawn from each box and their numbers added. What are the possible sums? Compute the probability of each sum.

Answer 1

Total number of slips in the first box = 5

Total number of slips in the second box = 5

Possible numbers in each box are 1, 2, 3, 4 and 5.

If one slip is drawn from any box, the possible numbers which can be obtained are 1, 2, 3, 4, and 5.

So, the possible sums which can be obtained can be found out by taking all the pairs one by one as follows:

i) When the number drawn from the first box is 1, the pairs obtained are:

Number Pair		Sum
(1, 1)		2
(1, 2)		3
(1, 3)		4
(1, 4)		5
(1, 5)		6

ii) When the number drawn from the first box is 2, the pairs obtained are:

Number Pair		Sum
(2, 1)		3
(2, 2)		4
(2, 3)		5
(2, 4)		6
(2, 5)		7

iii) When the number drawn from the first box is 3, the pairs obtained are:

Number Pair		Sum
(3, 1)		4
(3, 2)		5
(3, 3)		6
(3, 4)		7
(3, 5)		8

iv) When the number drawn from the first box is 4, the pairs obtained are:

Number Pair		Sum
(4, 1)		5
(4, 2)		6
(4, 3)		7
(4, 4)		8
(4, 5)		9

v) When the number drawn from the first box is 5, the pairs obtained are:

Number pair		Sum
(5, 1)		6
(5, 2)		7
(5, 3)		8
(5, 4)		9
(5, 5)		10

So the sums obtained are 2, 3, 4, 5, 6, 7, 8, 9 and 10.

Probability of obtaining the sum as 2 =

Probability of obtaining the sum as 3 =

Probability of obtaining the sum as 4 =

Probability of obtaining the sum as 5 =

Probability of obtaining the sum as 6 =

Probability of obtaining the sum as 7 =

Probability of obtaining the sum as 8 =

Probability of obtaining the sum as 9 =

Probability of obtaining the sum as 10 =