# Classical and Empirical Probability - Coin Tossing

1. Describe two main differences between classical and empirical probabilities.

Gather coins you find around your home or in your pocket or purse. You will need an even number of coins (any denomination) between 16 and 30. You do not need more than that. Put all of the coins in a small bag or container big enough to allow the coins to be shaken around. Shake the bag well and empty the coins onto a table. Tally up how many heads and tails are showing. Do ten repetitions of this experiment, and record your findings every time.

State how many coins you have and present your data in a table or chart.

Consider just your first count of the tossed coins. What is the observed probability of tossing a head? Of tossing a tail?

Show the formula you used and reduce the answer to lowest terms.

Did any of your ten repetitions come out to have exactly the same number of heads and tails? How many times did this happen?

2. How come the answers to the step above are not exactly 0.5 and 0.5?

3. What kind of probability are you using in this "bag of coins" experiment?

Compute the average number of heads from the ten trials (add up the number of heads and divide it by 10).

4. Change this to the average probability of tossing heads by putting the average number of heads in a fraction over the number of coins you used in your tosses.

5. Did anything surprising or unexpected happen in your results for this experiment?

Write the sample space for the outcomes of tossing three coins using H for heads and T for tails.

What is the probability for each of the outcomes?

Which kind of probability are we using here?

6. How come we do not need to have three actual coins to compute the probabilities for these outcomes?

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#### Solution Summary

This project deals with the similarities and differences between classical probability and empirical probability in a clear format with easily understandable written explanations to the calculations.

Classical and empirical probabilities are examined.

Please assist with the steps required to resolve the three statistical problems below?

1. In your own words, describe two main differences between classical and empirical probabilities.

2. Gather coins you find around your home or in your pocket or purse. You will need an even number of coins (any denomination) between 16 and 30. You do not need more than that. Put all of the coins in a small bag or container big enough to allow the coins to be shaken around. Shake the bag well and empty the coins onto a table. Tally up how many heads and tails are showing. Do ten repetitions of this experiment, and record your findings every time.

o State how many coins you have and present your data in a table or chart.

o Consider just your first count of the tossed coins. What is the observed probability of tossing a head? Of tossing a tail? Show the formula you used and reduce the answer to lowest terms.

o Did any of your ten repetitions come out to have exactly the same number of heads and tails? How many times did this happen?

o How come the answers to the step above are not exactly ½ and ½?

o What kind of probability are you using in this â??bag of coinsâ? experiment?

o Compute the average number of heads from the ten trials (add up the number of heads and divide it by 10).

o Change this to the average probability of tossing heads by putting the average number of heads in a fraction over the number of coins you used in your tosses.

o Did anything surprising or unexpected happen in your results for this experiment?

3. Write the sample space for the outcomes of tossing three coins using H for heads and T for tails.

o What is the probability for each of the outcomes?

o Which kind of probability are we using here?

o How come we do not need to have three actual coins to compute the probabilities for these outcomes?

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