# Probability Theory and Coins

1. In your own words, describe two main differences between classical and empirical probabilities. The differences between classical and empirical probabilities are that classical assumes that all outcomes are likely to occur, while empirical involves actually physically observing and collecting the information.

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. * State how many coins you have and present your data in a table or chart. For this experiment, I am using 20 coins.

ROLLS| HEADS (H)| TAILS (T)|

1| 10| 10|

2| 8| 12|

3| 5| 15|

4| 7| 13|

5| 11| 9|

6| 6| 14|

7| 9| 11|

8| 4| 16|

9| 11| 9|

10| 8| 12|

TOTALS| 79| 121|

* 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. On my first count of the tossed coins, the probability of heads showing was 10/20=1/2. The probability of tails showing was 10/20=1/2 * Did any of your ten repetitions come out to have exactly the same number of heads and tails? How many times did this happen? Yes and this on happen once, which was on my first roll.

* How come the answers to the step above are not exactly ½ and ½? Actually they are exactly ½ and ½.

* What kind of probability are you using in this “bag of coins” experiment? This experiment was empirical probability because I had to physically observe the information. * Compute the average number of heads from the...

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