There are a total of 4 tiles in the box.
The different possible outcomes when Kelly randomly chooses a tile are:
1. Kelly chooses tile 1
2. Kelly chooses tile 4
3. Kelly chooses tile 5
4. Kelly chooses tile 8
Since Kelly places the tile back in the box before choosing a second tile, the outcomes are independent of each other. Therefore, there are a total of 4 * 4 = 16 different possible outcomes when Kelly chooses two tiles.
Some examples of possible outcomes are:
- Kelly chooses tile 1 first, and then chooses tile 4 second
- Kelly chooses tile 4 first, and then chooses tile 4 again second
Each of these 16 outcomes has an equal probability of occurring, assuming that each tile has an equal chance of being chosen.
If we let X be the sum of the two tiles Kelly chooses, the possible values of X range from 2 (1+1) to 16 (8+8), with all values between 2 and 16 having a possibility of occurring.
The probability of each possible outcome can be calculated by counting the number of outcomes that result in that particular sum and dividing by the total number of outcomes (16).
For instance, the probability of Kelly choosing two tiles that add up to 9 (1+8, 8+1) would be 2/16 or 1/8.
Overall, the probability distribution of the sums of the two tiles chosen by Kelly can be determined by considering all possible outcomes and their respective probabilities.
A box contains four tiles, numbered 1, 4, 5, and 8 as shown. Kelly randomly chooses one tile, places it back in the box, then chooses a second tile.
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