Problem Statement:

Find the expected value of the sum of numbers on two tickets taken at random from five tickets numbered from 1 to 5.

Solution:

Let's first find all the possible combinations of two tickets that can be taken from five tickets numbered from 1 to 5.

1, 2
1, 3
1, 4
1, 5
2, 3
2, 4
2, 5
3, 4
3, 5
4, 5

There are a total of 10 possible combinations.

Now, let's find the sum of numbers on each of these combinations.

3
4
5
6
5
6
7
7
8
9

Next, we need to calculate the probability of each combination being selected.

The probability of selecting any two tickets is given by the formula:

P(selecting any two tickets) = (number of ways to select 2 tickets) / (total number of possible combinations)

= (5C2) / (10)

= 0.5

Therefore, the probability of selecting any two tickets is 0.5.

Finally, we can calculate the expected value of the sum of numbers on two tickets by using the formula:

Expected value = Σ (probability of each combination * sum of numbers on each combination)

= (0.5 * 3) + (0.5 * 4) + (0.5 * 5) + (0.5 * 6) + (0.5 * 5) + (0.5 * 6) + (0.5 * 7) + (0.5 * 7) + (0.5 * 8) + (0.5 * 9)

= 5.5

Therefore, the expected value of the sum of numbers on two tickets taken at random from five tickets numbered from 1 to 5 is 5.5.