Classical and Empirical Probabilities
1) Describe two main differences between classical and empirical probabilities. a. Classical probabilities are based on assumptions; Empirical probabilities are based on observations. b. Classical probabilities do not require an action to take place; Empirical probabilities have to have been “performed”.
2) Gather 16 to 30 coins. Shake and empty bag of coins 10 times and tally up how many head and tails are showing.
Number of coins: 20
* Consider the first toss, what is the observed probability of tossing a head? Of tossing a tail? Reduce to the lowest term. Tossing a Head: 11 / 20 Tossing a Tail: 9 / 20 The fractions are already in the lowest terms. * Did any of your repetitions have exactly the same number of heads and tails? Yes
* How many times did this happen? Once…10 heads and 10 tails (toss 5)
* Compute the average number of heads from the ten trials (add up the number of heads and divide it by 10). 11 + 8 +11 + 11+ 10 + 12 + 11 + 12 + 13 + 12 = 111 111 / 10 = 11.1 * 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.
11.1 / 20 = 0.555
* Did anything surprising or unexpected happen in your results for this experiment?
Yes, I did not expect to so many of the same results: 11H and 9T…4 times 12H and 8T…2 times
3) Write the sample space for the outcomes of tossing three coins using H for heads and T for tails.
H: heads T: tails (HHH, HHT, HTT, HTH, TTT, TTH, THT, THH)
P(E) = n(E) n(S) P(E) = ⅛
This is known as a classical probability
2) Gather 16 to 30 coins. Shake and empty bag of coins 10 times and tally up how many head and tails are showing.
Number of coins: 20
* Consider the first toss, what is the observed probability of tossing a head? Of tossing a tail? Reduce to the lowest term. Tossing a Head: 11 / 20 Tossing a Tail: 9 / 20 The fractions are already in the lowest terms. * Did any of your repetitions have exactly the same number of heads and tails? Yes
* How many times did this happen? Once…10 heads and 10 tails (toss 5)
* Compute the average number of heads from the ten trials (add up the number of heads and divide it by 10). 11 + 8 +11 + 11+ 10 + 12 + 11 + 12 + 13 + 12 = 111 111 / 10 = 11.1 * 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.
11.1 / 20 = 0.555
* Did anything surprising or unexpected happen in your results for this experiment?
Yes, I did not expect to so many of the same results: 11H and 9T…4 times 12H and 8T…2 times
3) Write the sample space for the outcomes of tossing three coins using H for heads and T for tails.
H: heads T: tails (HHH, HHT, HTT, HTH, TTT, TTH, THT, THH)
P(E) = n(E) n(S) P(E) = ⅛
This is known as a classical probability