A box contains 16 white and 16 black marbles. Construct a sample space for the experiment of randomly drawing out, with replacement, three marbles in succession and noting the color each time. (To draw “with replacement” means that each marble is put back before the next marble is drawn.)

To construct the sample space for this experiment, we need to consider all possible outcomes when drawing three marbles in succession with replacement from a box containing 16 white and 16 black marbles.

For each marble drawn, there are two possible outcomes: white (W) or black (B). We can represent the outcomes for each marble as a string of three letters, where each letter represents the color of the corresponding marble drawn.

Let's list all possible outcomes by considering all possible combinations of W and B for each marble:

1. WWW
2. WWB
3. WBW
4. WBB
5. BWW
6. BWB
7. BBW
8. BBB

These eight outcomes represent all possible results when drawing three marbles in succession with replacement from the box.

Hence, the sample space for this experiment consists of the following eight outcomes:
{WWW, WWB, WBW, WBB, BWW, BWB, BBW, BBB}

To construct the sample space for this experiment, we need to consider all the possible outcomes when drawing three marbles with replacement. Since there are 16 white and 16 black marbles, we will have two possible outcomes for each draw - either a white marble or a black marble.

Let's define W as a white marble and B as a black marble. Now, we can construct the sample space step by step:

For the first draw:
- W1 (denoting a white marble in the first draw)
- B1 (denoting a black marble in the first draw)

For the second draw:
- W1W2 (denoting white marbles in both the first and second draws)
- W1B2 (denoting a white marble in the first draw and a black marble in the second draw)
- B1W2 (denoting a black marble in the first draw and a white marble in the second draw)
- B1B2 (denoting black marbles in both the first and second draws)

For the third draw:
- W1W2W3 (denoting white marbles in all three draws)
- W1W2B3 (denoting white marbles in the first and second draws, and a black marble in the third draw)
- W1B2W3 (denoting a white marble in the first draw, a black marble in the second draw, and a white marble in the third draw)
- W1B2B3 (denoting a white marble in the first draw, black marbles in the second and third draws)
- B1W2W3 (denoting a black marble in the first draw, white marbles in the second and third draws)
- B1W2B3 (denoting a black marble in the first draw, a white marble in the second draw, and a black marble in the third draw)
- B1B2W3 (denoting black marbles in the first and second draws, and a white marble in the third draw)
- B1B2B3 (denoting black marbles in all three draws)

This completes the construction of the sample space for the experiment of drawing three marbles in succession and noting the color each time.

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(white,black)