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

Answer:

If you flip 2 coins the possible results are:

H1 H2, H1 T2, T1 H2 and T1 T2      there no other possibilities

So the probability of H H is 1/4 as tis he probability of T T.

The probability of an H and a T is 2/4 or 1/2.

The total probability adds to 1 as it must.

So, theoretically, in 100 tosses you should get

25 HH, 25, TT and 50 HT.

This will differ from the experimental values because the experimental results occur randomly.

In more advanced probability theory, the results are expected to form

what is called a bell curve which would be the expected results of a very large number of tosses, with  different curves for HT and HH. Taking HH

one would expect most of the results to cluster around the middle of the

curve, which is the top of the bell with a probability of 1/2. Large variations from the expected result would form the lower portions of the bell or be in one of the tails of the curve.