Question

Instructions
For this activity, you will need two different 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.
Flip two different coins 100 times, and record the results of each coin toss in a table like the one below:
Result
Frequency
Two heads 30

Two tails 40

One head, one tail 70


Answer the following questions based on the data you gathered. You must show your work to receive credit.
What is the theoretical probability that a coin toss results in two heads showing?
What is the experimental probability that a coin toss results in two heads showing?
What is the theoretical probability that a coin toss results in two tails showing?
What is the experimental probability that a coin toss results in two tails showing?
What is the theoretical probability that a coin toss results in one head and one tail showing?
What is the experimental probability that a coin toss results in one head and one tail showing?
Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?

Answer 1

The experimental probability that a coin toss results in two heads showing is 3/14

The theoretical probability of two heads

The sample space of two coins is:

S = {HH, HT, TH, TT}

In the above sample space, we have:

• n(HH) = 1 i.e. number of two heads
• Total = 4 i.e. the sample size

The theoretical probability of two heads is calculated as:

P = n(HH)/Total

This gives

P = 1/4

Hence, the theoretical probability of two heads is 1/4

The experimental probability of two heads?

To do this, we make use of the table in the question

The table is given as:

Result                                  Frequency

Two heads (HH)                     30

Two tails  (TT)                        40

One head, one tail (HT)        70

Total                                     140

The experimental probability of two heads is calculated as:

P = n(HH)/Total

This gives

P = 30/140

Simplify

P = 3/14

Hence, the experimental probability of two heads is 3/14

The theoretical probability of two tails

Using the sample space in (a), we have:

• n(TT) = 1 i.e. number of two tails
• Total = 4 i.e. the sample size

The theoretical probability of two tails is calculated as:

P = n(TT)/Total

This gives

P = 1/4

Hence, the theoretical probability of two tails is 1/4

The experimental probability of two tails

From the table in the question, we have:

Two tails  (TT)  =40

Total = 140

The experimental probability of two tails is calculated as:

P = n(TT)/Total

This gives

P = 40/140

Simplify

P = 2/7

Hence, the experimental probability of two tails is 2/7

The theoretical probability of one head and one tail

Using the sample space in (a), we have:

• n(HT) = 2 i.e. number of one head and one tail
• Total = 4 i.e. the sample size

The theoretical probability of one head and one tail is calculated as:

P = n(HT)/Total

This gives

P = 2/4

Simplify

P = 1/2

Hence, the theoretical probability of one head and one tail is 1/2

The experimental probability of one head and one tail

From the table in the question, we have:

One head one tail  (HT)  = 70

Total = 140

The experimental probability of one head one tail is calculated as:

P = n(HT)/Total

This gives

P = 70/140

Simplify

P = 1/2

Hence, the experimental probability of one head one tail is 1/2

Why are there difference between the theoretical probabilities and the experimental probabilities?

The reason for the difference between the probability types is because one is as a result of an actual experiment, while the other is an estimate of the experiment.

Read more about probability at:

https://brainly.com/question/251701

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