Question

Flip two coins 100 times, and record the results of each coin toss in a table like the one below:

Answer 1

Answer:

1)The theoretical probability that a coin toss results in two heads showing is 25%.

2)The experimental probability that a coin toss results in two heads showing is 44%.

3) The theoretical probability that a coin toss results in two tails showing is 25%.

4) The experimental probability that a coin toss results in two tails showing is 34%.

5) The theoretical probability that a coin toss results in one head and one tail showing is 50%.

6) The experimental probability that a coin toss results in a head and a tail is 22%.

7) The experimental probabilities are slightly different from the theoretical probabilities because the number of experiments is relatively small. As the number of experiments increase, the experimental probabilities will get closer to the theoretical probabilities.

Step-by-step explanation:

Probability:

What you want to happen is the desired outcome.

Everything that can happen iis the total outcomes.

The probability is the division of the number of possible outcomes by the number of total outcomes.

Theoretical Probability:

The results you expect to happen.

Experimental Probability:

The probability determined from the result of an experiment.

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

In each toss, the theoretical  probability that a coin toss results in a head showing is 50%.

So for two coins, the probability is:

$P = (0.5)^{2} = 0.25$

The theoretical probability that a coin toss results in two heads showing is 25%.

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

There were 100 flips, and it resulted in two heads 44 times, so:

$P = \frac{44}{100} = 0.44$

The experimental probability that a coin toss results in two heads showing is 44%.

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

In each toss, the theoretical  probability that a coin toss results in a tail showing is 50%.

So for two tails, the probability is:

$P = (0.5)^{2} = 0.25$

The theoretical probability that a coin toss results in two tails showing is 25%.

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

There were 100 flips, and it resulted in two tails 34 times, so:

$P = \frac{34}{100} = 0.34$

The experimental probability that a coin toss results in two tails showing is 34%.

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

In each toss, the theoretical probability that a coin toss results in a tail showing is 50% and in a head showing is 50%.

They can be permutated, as the tail can appear before the head, or the head before the tail. So:

$P = p_{2,1}*(0.5)*(0.5) = \frac{2!}{1!}*0.25 = 0.50$

The theoretical probability that a coin toss results in one head and one tail showing is 50%.

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

There were 100 flips, and it resulted in a head and a tail showing 22 times, so:

$P = \frac{22}{100} = 0.22$

The experimental probability that a coin toss results in a head and a tail is 22%.