Probability: Coin Tossing Project
Student’s name:
Institutional Affiliation:
Introduction
Probability is very essential in determining the likeliness with which an event may or may not take place. It plays an important role in various fields but has been implemented widely in gambling. The con tossing project is aimed at determining the highest level of success with which a particular event carried out multiple times would bare.
The guesses were aimed at setting projection that would be compared against the calculated value to help determine the accuracy of probability calculations. The calculated values, just like the guesses are projections that cannot repeat themselves and are used to gauge the relationship …show more content…
(You will need to include all of the answers to the questions below in your paper.)
1. What percent of the time do you expect to get 5 heads? ___25%_________
2. What percent of the time do you expect to get 3 heads? ___12%_________
3. What percent of the time do you expect to get 7 heads? _____12%_______
4. What percent of the time do you expect to get no heads? ____1%________
5. What percent of the time do you expect to get all heads? _______1%_____
6. Use your guesses above to fill in the chart below for all of the outcomes.
X = Heads 0 1 2 3 4 5 6 7 8 9 10
Prob(X) 0.001 0.01 0.04 0.12 0.21 0.25 0.21 0.12 0.04 0.01 0.001
7. Adjust your guesses for 1-6 above until the two rules of probability are satisfied (Each value is between 0 and 1 and the sum of all of the probabilities is 1).
X = Heads 0 1 2 3 4 5 6 7 8 9 10
Prob(X) 0.001 0.01 0.04 0.12 0.205 0.25 0.205 0.12 0.04 0.01 0.001
8. What is the expected value for heads after tossing 600 coins? ______60______
9. How is the probability of getting three heads (# 2 above) related to the probability of getting three tails (# 3 above)? Explain your answer.
The probability of getting three heads and three tails are not related at all since the coin flipping practice is a mutually exclusive …show more content…
The graph comparing the results between the guesses and computational values shows a very minute discrepancies. The small differences provides confidence in the probability computation process. Comparisons from guesses, empirical and computational values did not bear any resemblance at all. The event that ten coins will give a certain number of heads and/or tails is purely unique and cannot be precisely determined under whatever circumstances. The lesson learnt from the project is that the future of certain events with equal chances of occurring cannot be predetermined. The outcomes of gambling games and casinos can never be predetermined by the players if the playing process is not tampered with in a way. Winnings resulting from all fair gambling processes are therefore pure luck.
Appendix B
Toss number Number of heads Cumulative Heads Total coins tossed Cumulative % heads
1 3 3 10 0.3000
2 3 6 20 0.3000
3 4 10 30 0.3333
4 4 14 40 0.3500
5 6 20 50 0.4000
6 6 26 60 0.4333
7 6 32 70 0.4571
8 7 39 80 0.4875
9 8 47 90 0.5222
10 7 54 100 0.5400
11 3 57 110 0.5182
12 6 63 120
Student’s name:
Institutional Affiliation:
Introduction
Probability is very essential in determining the likeliness with which an event may or may not take place. It plays an important role in various fields but has been implemented widely in gambling. The con tossing project is aimed at determining the highest level of success with which a particular event carried out multiple times would bare.
The guesses were aimed at setting projection that would be compared against the calculated value to help determine the accuracy of probability calculations. The calculated values, just like the guesses are projections that cannot repeat themselves and are used to gauge the relationship …show more content…
(You will need to include all of the answers to the questions below in your paper.)
1. What percent of the time do you expect to get 5 heads? ___25%_________
2. What percent of the time do you expect to get 3 heads? ___12%_________
3. What percent of the time do you expect to get 7 heads? _____12%_______
4. What percent of the time do you expect to get no heads? ____1%________
5. What percent of the time do you expect to get all heads? _______1%_____
6. Use your guesses above to fill in the chart below for all of the outcomes.
X = Heads 0 1 2 3 4 5 6 7 8 9 10
Prob(X) 0.001 0.01 0.04 0.12 0.21 0.25 0.21 0.12 0.04 0.01 0.001
7. Adjust your guesses for 1-6 above until the two rules of probability are satisfied (Each value is between 0 and 1 and the sum of all of the probabilities is 1).
X = Heads 0 1 2 3 4 5 6 7 8 9 10
Prob(X) 0.001 0.01 0.04 0.12 0.205 0.25 0.205 0.12 0.04 0.01 0.001
8. What is the expected value for heads after tossing 600 coins? ______60______
9. How is the probability of getting three heads (# 2 above) related to the probability of getting three tails (# 3 above)? Explain your answer.
The probability of getting three heads and three tails are not related at all since the coin flipping practice is a mutually exclusive …show more content…
The graph comparing the results between the guesses and computational values shows a very minute discrepancies. The small differences provides confidence in the probability computation process. Comparisons from guesses, empirical and computational values did not bear any resemblance at all. The event that ten coins will give a certain number of heads and/or tails is purely unique and cannot be precisely determined under whatever circumstances. The lesson learnt from the project is that the future of certain events with equal chances of occurring cannot be predetermined. The outcomes of gambling games and casinos can never be predetermined by the players if the playing process is not tampered with in a way. Winnings resulting from all fair gambling processes are therefore pure luck.
Appendix B
Toss number Number of heads Cumulative Heads Total coins tossed Cumulative % heads
1 3 3 10 0.3000
2 3 6 20 0.3000
3 4 10 30 0.3333
4 4 14 40 0.3500
5 6 20 50 0.4000
6 6 26 60 0.4333
7 6 32 70 0.4571
8 7 39 80 0.4875
9 8 47 90 0.5222
10 7 54 100 0.5400
11 3 57 110 0.5182
12 6 63 120