Question

Theoretical Probabilities of Repeated Events Practice
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Question
James used a table to determine the sample space for an experiment in which a purple (P) or yellow (Y) marble is selected from a bag 4 times and replaced after each draw.

Row 1 PPPP PPPY PPPY PPYP
Row 2 PYPP YPPP PYPY YPYP
Row 3 YYYY YYYP YYPY YPYY
Row 4 PYYY YYPP PPYY PYYP
In which row did James make an error when he created his table? Answer 1 for row 1, 2 for row 2, 3 for row 3, or 4 for row 4.

(1 point)

Answer 1

To determine if there is an error in the rows of James's table, we need to consider the possible combinations of drawing a purple (P) or yellow (Y) marble four times while replacing after each draw.

Each draw has 2 possible outcomes: P or Y. Therefore, for 4 draws, the total possible combinations (sample space) is \(2^4 = 16\).

Let's analyze the rows:

1. **Row 1:**
- PPPP
- PPPY
- PPPY
- PPYP
- This row includes 4 combinations, but "PPPY" is listed twice, which means this row has a duplicate and does not represent unique combinations properly.

2. **Row 2:**
- PYPP
- YPPP
- PYPY
- YPYP
- This row has 4 unique combinations, which is correct.

3. **Row 3:**
- YYYY
- YYYP
- YYPY
- YPYY
- This row also has 4 unique combinations, which is correct.

4. **Row 4:**
- PYYY
- YYPP
- PPYY
- PYYP
- This row has 4 unique combinations, which is correct.

The error occurred in **Row 1**, where the combination "PPPY" was repeated. Therefore, the answer is:

**1**