Probability Theory and Coins Essay
Week Four Discussion 2 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 ? and ?? Actually they are exactly ? and ?. * 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 ten trials (add up the number of heads and divide it by 10). 79/10 = 7. 9 * 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. 79/200= . 395 round to . 4 .4 x 100% = . 4 = 40% chance of coming up with heads * Did anything surprising or unexpected happen in your results for this experiment? Yes. I did not expect any of the rolls to come out half and half, much less my first roll. . 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? (HHH, HHT, HTT, TTT) There would be only four possible results from three coins. Therefore, there would be ? chance of occurrence. * Which kind of probability are we using here? Classical probability because one can assume it. * How come we do not need to have three actual coins to compute the probabilities for these outcomes? Because with the small amount of coins, one can assume the likely outcome.