Question

A student wants to simulate a fair coin toss using a random digit table. She selects the numbers 0-4 to represent heads and 5-9 to represent tails and selects samples of 10. What are the results of her first 3 trials?

84164 91333
90954 87186
31598 25942

A) Trial: 1, 2, 3; Heads: 7, 3, 5; Tails: 3, 7, 5
B) Trial: 1, 2, 3; Heads: 3, 7, 4; Tails: 7, 3, 6
C) Trial: 1, 2, 3; Heads: 7, 4, 6; Tails: 3, 6, 4
D) Trial: 1, 2, 3; Heads: 3, 7, 5; Tails: 7, 3, 5

Answer 1

To determine the results of the trials, we need to analyze each group of digits selected by the student based on her criteria for representing heads and tails.

- Heads (0-4): The digits that fall within this range will be counted as heads.
- Tails (5-9): The digits that fall within this range will be counted as tails.

Let's analyze the three trials given:

1. **Trial 1: 84164 91333**

- Counting heads (0-4): 4, 1, 4 (3 heads)
- Counting tails (5-9): 8, 6, 9, 3, 3 (7 tails)

**Results: Heads: 3, Tails: 7**

2. **Trial 2: 90954 87186**

- Counting heads (0-4): 0, 4 (2 heads)
- Counting tails (5-9): 9, 9, 5, 8, 7, 1, 8, 6 (8 tails)

**Results: Heads: 2, Tails: 8**

3. **Trial 3: 31598 25942**

- Counting heads (0-4): 3, 1, 2, 2, 3 (5 heads)
- Counting tails (5-9): 5, 9, 8, 4 (4 tails)

**Results: Heads: 5, Tails: 4**

Now, let's summarize the findings:

- **Trial 1:** Heads: 3, Tails: 7
- **Trial 2:** Heads: 2, Tails: 8
- **Trial 3:** Heads: 5, Tails: 4

Looking at these results, we can compare them to the options given:

A) Trial: 1, 2, 3; Heads: 7, 3, 5; Tails: 3, 7, 5
B) Trial: 1, 2, 3; Heads: 3, 7, 4; Tails: 7, 3, 6
C) Trial: 1, 2, 3; Heads: 7, 4, 6; Tails: 3, 6, 4
D) Trial: 1, 2, 3; Heads: 3, 7, 5; Tails: 7, 3, 5

None of these options match the results from the analysis.

To clarify, the results from the analysis should be revised as follows:

1) Heads: 3, Tails: 7
2) Heads: 2, Tails: 8
3) Heads: 5, Tails: 4

Hence none of the provided answer options (A, B, C, or D) are correct based on the simulated trials.