Flip two coins 100 times, and record the results of each coin toss in a table like the one below: result frequency two heads 42 two tails 37 one head, one tail 21 answer the following questions based on the data you gathered. you must show your work to receive credit. 1. what is the theoretical probability that a coin toss results in two heads showing? 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? answer all of theese!

Result      Frequency
Two heads          36
Two tails               25
One head, One tail 39

1. What is the theoretical probability that a coin toss results in two heads showing?
1/2 * 1/2 = 1/4 = 0.25

2. What is the experimental probability that a coin toss results in two heads showing?
36/100 = 0.36

3. What is the theoretical probability that a coin toss results in two tails showing?
1/2 * 1/2 = 1/4 = 0.25

4. What is the experimental probability that a coin toss results in two tails showing?
25/100 = 0.25

5. What is the theoretical probability that a coin toss results in one head and one tail showing
1/2 = 0.5

6. What is the experimental probability that a coin toss results in one head and one tail showing?
39/100 = 0.39

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

The experimental probabilities do not always match the theoretical probability because of chance. But the more coin flips we do, we expect the experimental probability to get closer to the theoretical probability.

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