The basics of probability is fun to both learn and teach because you can use real-life examples. Playing the game of business or monopoly or snakes and ladders with your children? Why not use the single or two-die system to teach them probability? It’s the best way to make them understand the mathematical concept and teach them why it is an important part of everyday life, economics, computing, and many other professional fields.
You can also demonstrate how probability works, when there is more than one influencing factor. The perfect example of this is the use of two dice in a game. When probability depends on multiple factors, it automatically makes the calculations complex, but not when you show it using examples.
So, here’s a quick look at how you can use dice to show what probability is and what is the chance of rolling a 7 when you play a game. But before getting to the specifics, here’s a take on the basics.
What Is Probability?
Probability is the likelihood of a random event occurring. It is a part of data mathematics and is generally used to predict events and their occurrence in finance, economics, and anything related to numbers. Probability, in the most basic level, is denoted as a value between 0 and 1. However, percentages are also used to signify the probability of an event. For example, the probability of a student winning a competition where 10 people participated is 10%. This can also be denoted as 0.1.
Probability is used to calculate the chance of an event occurring when the outcome is unclear. The popular example of a die can be used to demonstrate this.
- Pick a die
- Before you roll it, can you predict which number will turn up?
Sure, you can guess a number, but can you guarantee that the number you guessed will turn up? Even if it appears the first time by a stroke of luck, how can you ensure the same thing in the next roll?
This is the quandary that the concept of probability solves. You can calculate the probability of any number appearing and attribute a percentage to it.
Since a die has the possibility of 6 different numbers (1, 2, 3, 4, 5, 6) appearing, the probability can be calculated this way:
- Count the sample space i.e. the total number of events that can occur. In the case of a die, this is 6 because any of the 6 numbers can come up when you roll it
- Count the number of times a said event can occur. Assume that the number 5 has to appear. In the case of this die, the chance of the number 5 appearing is 1
- Use these two figures (or data) to calculate the probability i.e. the number of times the event can occur should be divided by the sample space (1/6)
The answer is 1/6, which converts to 0.167 or 16.67%. Therefore, the probability of getting the number 5 to appear after rolling a die is 16.67%. The same is true for all the other numbers because the number of times any of the 6 numbers can appear is always once.
Pro Tip – You can calculate the sample size for a die rolling game using the squared method. A die always has 6 numbers. So, depending upon the number of dice being used, simply square the number to calculate the sample space. 6^2=36 for two dice, 6^3=216 for three dice, and so on.
As you can see, this example uses two types of specific data to calculate the probability. While probability itself is a type of quantitative data, it is calculated using specific data sets to derive more information. You can learn more about what is data and its different types at Cuemath, an online mathematics portal for students of all grades. Your child can read up about different types of data such as mean, median, mode, permutations and combinations, and data handling.
Try applying this formula to another example. If you run the same technique when you flip a coin, the following will be the answer:
- Getting a heads – 0.5 or 50%
- Getting a tails – 0.5 or 50%
This is the gist of how probability works. It allows you to find an estimated value of an event occurring. It can be applied to any calculation where there is more than one event involved. You can solve the main question using this technique. Here’s how.
What is the Probability of Rolling a 7?
For this, you will need two dice. This is because a single die only has 6 faces/numbers. Two dice have a total of 12 faces/numbers.
Here’s how you can calculate the probability of rolling a 7:
- Calculate the sample space: Numbers 2 to 12 can appear but they can in different combinations. For example, the number 5 can appear in the following ways:
- First die showing 1, second die showing 4
- First die showing 2, second die showing 3
- First die showing 3, second die showing 2
- First die showing 4, second die showing 1
- This makes the sample space as 36. This is because when you roll two dice, there are 36 different possible combinations
- Calculate the number of times the number 7 can appear:
- First die showing 1, second die showing 6
- First die showing 2, second die showing 5
- First die showing 3, second die showing 4
- First die showing 4, second die showing 3
- First die showing 5, second die showing 2
- First die showing 6, second die showing 1
- This makes the number of times the number 7 can appear as 6
- As per the above calculation, the probability of rolling a 7 can be derived when you divide 6 with 36. This translates to 6/36 i.e. 0.167 or 16.67%
As you can see, you can easily calculate the probability of rolling any number using the formula. You just need two data sets: the total sample space and the number of times an event can occur.
Interestingly, the probability of rolling a 6 or an 8 is both the same when you roll two dice. This is because the number of times or ways in which those two numbers can appear is the same i.e. 5.
For getting a 6, these are the combinations:
- First die showing 1, second die showing 5
- First die showing 2, second die showing 4
- First die showing 3, second die showing 3
- First die showing 4, second die showing 1
- First die showing 5, second die showing 1
The same is true when you calculate it for number 8:
- First die showing 2, second die showing 6
- First die showing 3, second die showing 5
- First die showing 4, second die showing 4
- First die showing 5, second die showing 3
- First die showing 6, second die showing 2
Using 3 Dice
As you increase the number of dice, the calculation becomes more complex. Here’s a quick look at how the calculation changes when you roll three dice. The probability of rolling a 7 using 3 dice is demonstrated below:
- Total sample space: 216
- Number of times 7 can appear: 15
- Probability: 15/216 i.e. 0.069 or 6.94%
If you observe, the probability percentage changes drastically when there is an extra influencing element. The probability of rolling a 7 is 16.67% when you roll two dice. It goes down to 6.94% when you roll three dice. It will further go down if you roll four dice.
This is because of the increase in sample space size and the decrease in the number of possible outcomes for that specific number.
Learning becomes easy when you use real-life examples. It becomes even easier and fun when it is part of a game that you can play with your child. Cuemath is one such platform where your child can stay engaged and learn all the mathematical concepts for their specific grade using animated examples and easy-to-solve games. It uses colourful images and child-friendly examples to teach basic mathematical concepts so that you don’t have to sit down and push them to study.
Topics such as probability can be difficult to understand at first, which is why it is important to make learning fun and enjoyable. Head to Cuemath today and explore the most effective way to teach your child mathematics.
Just like how you learned to find the probability of rolling a 7, your child and you can learn and solve simple Maths problems using Cuemath.