Final answer:
To find the probability of getting a sum greater than seven when choosing two tiles, we count the favorable outcomes and divide by the total number of possible outcomes. In this case, there are 4 favorable outcomes (9, 9, 6, 9) out of 16 possible outcomes, resulting in a probability of 0.25.
Step-by-step explanation:
To find the probability that the sum of two chosen tiles is greater than seven, we need to determine the number of favorable outcomes and the total number of possible outcomes.
There are four tiles in the box: one, four, five, and eight. When we choose the first tile, it can be any of the four options. After placing it back in the box, the second tile can also be any of the four options. Therefore, there are a total of 4 * 4 = 16 possible outcomes.
Now, let's count the favorable outcomes where the sum of the two tiles is greater than seven:
- If we choose the tile eight first, the only favorable outcome is choosing the tile one next (8 + 1 = 9).
- If we choose the tile five first, there are two favorable outcomes: choosing the tile four or the tile one next (5 + 4 = 9, 5 + 1 = 6).
- If we choose the tile four first, there is one favorable outcome: choosing the tile five next (4 + 5 = 9).
- If we choose the tile one first, there are no favorable outcomes since the other tiles are all less than or equal to seven.
Therefore, there are a total of 1 + 2 + 1 = 4 favorable outcomes.
The probability of getting a sum greater than seven is calculated by dividing the number of favorable outcomes by the total number of possible outcomes: 4 / 16 = 1 / 4 = 0.25.