Question

flip a coin 30 times and document the result of each toss. Then provide both empirical and theoretical proability distributions. use the appropriate expression for probability.

Answer 1

The table below are the experimental data when a coin is flip 30 times :

Event	Number of times
Head (H)	12
Tail (T)	18

Empirical Probability

When you gather data from observations during an experiment, you will be calculating an empirical (or experimental) probability.

The empirical (or experimental) probability of an event is an "estimate" that an event will occur based upon how often the event occurred after collecting data from an experiment in a large number of trials. This type of probability is based upon direct observations. Each observation in an experiment is called a trial.

For the given experiment,

Let E : event of getting head

Number of times the event H occur = 12

Total number of trials = 30

Then

Theoretical probability

With theoretical probability, you do not actually conduct an experiment. Instead, you use what you know about the situation to determine the probability of an event occurring. You may use your reasoning skills or an existing formula to arrive at your answer.

The theoretical probability of an event occurring is an "expected" probability based upon knowledge of the situation. It is the number of favorable outcomes to the number of possible outcomes.

Let

E : Event of getting Head

Possible outcomes when tossing a coin = {H,T}

so,number of possible outcome =2

Number of favorable outcomes ( getting H ) = 1

Therefore,

Empirical (experimental) probability approaches theoretical probability when the number of trials is extremely large.