Theoretical Probability and Experimental Probability Coin toss, need help!

Question

For this activity, you will need two coins. First, you will determine the theoretical probability of events. Then, you will flip the coins 100 times and determine the experimental probability of the events.

Here are the results for my coin flips

Two heads | 23

Two Tails| 30

One head, one tail | 47

Now answer these questions based on the data above

1. What is the theoretical probability that a coin toss results in two heads showing? 2

2. What is the experimental probability that a coin toss results in two heads showing?

3. What is the theoretical probability that a coin toss results in two tails showing?

4. What is the experimental probability that a coin toss results in two tails showing?

5. What is the theoretical probability that a coin toss results in one head and one tail showing?

6. What is the experimental probability that a coin toss results in one head and one tail showing?

7. Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?

I need you to explain as well as possible because this is sorta hard for me to understand. Thank you!

Answer 1

1) 1/4 = 0.25 = 25%

2) 23/100 = 23%

3) 1/4 = 0.25 = 25%

4) 30/100 = 30%

5) 1/2 = 0.5 = 50%

6) 47/100 = 47%

7) 2 heads: 23% - 25% = -2% error

2 tails: 30% - 25% = 5% error

1 of each: 47% - 50% = -3% error

as the number of trials increases to infinity, the experimental probability shall

become very close to the theoretical probability. Law of Large Numbers