One of the origins of of probability as a field in mathematics was solving games of chance. The famous correspondence between Fermat and Pascal in 1654 was one of the earliest accounts on how to use mathematics formally in order to solve a fair game of chance.
In this post, we are going to design a game that will demonstrate the power of probability. We will use probability to create a game that looks like as if it favors the player, while in reality, it favors the casino. Although most casino games actually obviously favor the casino, the game below is a bit more conservative (or should I say ‘deceptive.’)
The dice to be used in the game below is the standard 6-sided die whose number of dots are from 1 to 6. This means that the smallest possible sum is 1 + 1 = 2 and the largest possible sum is 6 + 6 = 12. Below are the instructions on how to play the game. Continue reading
Last week, we have completed the 5-part Experimental and Theoretical Probability Series. To those who have not read it, below is the list of posts.
- Experimental and Theoretical Probability Part 1. This post discusses about the sum of the number of dots of two rolled standard cubical dice. A spreadsheet is used to simulate the rolling 1000 times and sums are recorded and tallied. A step-by-step instruction in doing the simulation is provided.
- Experimental and Theoretical Probability Part 2. This post confirms the findings in Part 1. Two more experiments are conducted — the first one is rolling the dice 2000 times, and the other is rolling it again 3000 times.
- Experimental and Theoretical Probability Part 3. The third part is a discussion on why the findings in Part 1 and Part 2 are such. The ways of getting a particular sum is discussed in this post.
- Experimental and Theoretical Probability Part 4. The fourth part discusses the relationships between the experiments and the findings in Part 3. The formal definitions of Experimental and Theoretical probabilities are also discussed here.
- Experimental and Theoretical Probability Part 5. The fifth part summarizes the series and give real-life examples that use experimental and theoretical probability.
I hope you have enjoyed reading this series. Watch out for more Math and Multimedia Tutorial Series.
This is the fifth and the final part of the Experimental and Theoretical Probability Series. In this post, we are going to summarize what we have discussed in the previous four posts, and we are going to talk about some real-life applications of experimental and theoretical probability.
Standard Cubical Dice
Experimental Probability, as we have discussed in the fourth part of this series, may be obtained by conducting experiments and recording the results. It is the ratio of the number of times an event occurs to the total number of trials. In the first part of this series, we experimented rolling to dice 1000 times (via a spreadsheet) and we tallied the sums. We recorded the that sum 2 occurred 29 times out of 1000 trials. We can say that the experimental probability of getting a 2 from that particular experiment is 29/1000. Continue reading
This the second part of the series of posts on Experimental and Theoretical Probability.
In the first part of this series, we used a spreadsheet to simulate the rolling of dice 1000 times and automatically recorded the sums. We have observed that the sum frequencies are not evenly distributed (see Figure 1).
In rolling the two dice 1000 times, for example, we rolled a seven 156 times, while we only rolled a two 29 times. Well, we want to think that this is just a coincidence, so maybe we could try it one more time. Continue reading
This the first part of the series of posts on Experimental and Theoretical Probability.
If two standard cubical dice are rolled, one red and one blue, the possible sums ranges from 2 = (1+1) and 12 = (6+6).
Now, are the chances of getting these 11 sums equal? For example, is the chance of getting a sum of 2 similar to the chance of getting a sum of 5?
Let us try to roll the two dice 1000 times. Of course, we will not do this manually. Continue reading