Probability
Probability 2
Theory
Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. (Feller, 1966) One object of probability theory is random variables. An individual coin toss would be considered to be a random variable. I predict if the coin is tossed repeatedly many times the sequence of it landing on either heads or tails will be about even.
Experiment
The Experiment we conducted was for ten students to flip a coin one hundred times each and record each time if we got heads or tails.
• The first step was to count the total number of Heads and Tails flipped.
• The second step was to draw circles around consecutive groups of heads and consecutive groups of tails.
• The third step was to count the number of consecutive flips in each cluster.
• The fourth step is to count the clusters.
Analysis
The graph shows the number of consecutive heads or tails from groups of 1 through 10 the coin landed on. On the average, heads was landed on 48.2% of the time, and tails 51.8% of the time.
Conclusion
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to
Probability 3
become closer as more trials are performed. Our prediction was right the more we flipped the coin the closer our results got to a fifty fifty split.
Theory
Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. (Feller, 1966) One object of probability theory is random variables. An individual coin toss would be considered to be a random variable. I predict if the coin is tossed repeatedly many times the sequence of it landing on either heads or tails will be about even.
Experiment
The Experiment we conducted was for ten students to flip a coin one hundred times each and record each time if we got heads or tails.
• The first step was to count the total number of Heads and Tails flipped.
• The second step was to draw circles around consecutive groups of heads and consecutive groups of tails.
• The third step was to count the number of consecutive flips in each cluster.
• The fourth step is to count the clusters.
Analysis
The graph shows the number of consecutive heads or tails from groups of 1 through 10 the coin landed on. On the average, heads was landed on 48.2% of the time, and tails 51.8% of the time.
Conclusion
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to
Probability 3
become closer as more trials are performed. Our prediction was right the more we flipped the coin the closer our results got to a fifty fifty split.