Question

Please complete the following question:




In an experiment, a coin is flipped 30 times and the results are as follows:

{H, H, H, T, T, T, T, H, T, H, H, T, H, H, H, T, T, H, H, H, T, H, T, T, H, T, H, H, H, H}.

Heads: 18

Tails: 12

(2 points)
Round your answer to the tenth place (one digit).

Determine the experimental P(head) =
.

Determine the theoretical P(head) =
.

Question 2
(1 point)
The theoretical probability is
the experimental probability the coin landing on heads.

Answer 1

To determine the experimental and theoretical probabilities, let's go through the calculations step by step.

**Experimental Probability of Heads (P(head))**:

The experimental probability is calculated using the formula:

\[
P(head) = \frac{\text{Number of Heads}}{\text{Total Flips}}
\]

From the provided data:
- Number of Heads = 18
- Total Flips = 30

Now, substituting the values:

\[
P(head) = \frac{18}{30} = 0.6
\]

**Rounded to the tenth place**:

\[
P(head) = 0.6
\]

---

**Theoretical Probability of Heads (P(head))**:

For a fair coin, the theoretical probability of landing on heads is:

\[
P(head) = \frac{1}{2} = 0.5
\]

---

**Answers**:

1. **Experimental P(head)** = 0.6
2. **Theoretical P(head)** = 0.5

---

**Question 2**: The theoretical probability is **not equal to** the experimental probability of the coin landing on heads.

Explanation: The experimental probability (0.6) is greater than the theoretical probability (0.5) in this experiment.