Question

follow these steps to perform a probability experiment.

1. what is the experimental probability of flipping a head after twenty flips of the coin? 9/20
2. what is the theoretical probability of flipping a head? 1/2
3. press the button to flip the coin 80 more times
4. as the number of flips increases, the difference between the experimental probability and theoretical probability

• decreases
• remains constant
• increases

Explanation:

Step1: Recall the law of large numbers

The law of large numbers states that as the number of trials in a probability - experiment increases, the experimental probability approaches the theoretical probability.

Step2: Analyze the relationship

In the case of coin - flipping, the theoretical probability of getting a head is $\frac{1}{2}$. As the number of flips (trials) increases, the experimental probability (the proportion of heads in the actual flips) gets closer to the theoretical probability. So the difference between them decreases.

Answer:

decreases