The Ultimate Guide to Probability in the 11 Plus Math Exam: Everything You Need to Know

Key concepts and terms in probability

Probability is the branch of mathematics that deals with the study of random events. In the 11 Plus Math Exam, probability questions can come in various forms and require different levels of understanding. Before diving into the different types of probability problems, it is essential to understand some key concepts and terms.

Sample space

The sample space is the set of all possible outcomes of an experiment. For example, when rolling a dice, the sample space would be {1, 2, 3, 4, 5, 6}.

Event

An event is any subset of the sample space. For example, rolling an even number on a dice would be an event, and its subset would be {2, 4, 6}.

Outcome

An outcome is a particular result of an experiment. For example, rolling a 4 on a dice is an outcome.

Probability

Probability is a measure of the likelihood of an event occurring. It is represented as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.

Understanding probability notation

To express probability, mathematicians use a notation that consists of a fraction, decimal, or percentage. The notation is as follows:

P(Event) = Number of favourable outcomes / Total number of possible outcomes

For example, the probability of rolling a 3 on a dice is:

P(Rolling a 3) = 1 / 6 = 0.1667 = 16.67%

Probability rules and formulas

There are several rules and formulas that you need to know to solve probability problems in the 11 Plus Math Exam. Here are some of the most important ones:

Addition rule

The addition rule states that the probability of two or more events occurring is the sum of their individual probabilities minus the probability of their intersection.

P(A or B) = P(A) + P(B) - P(A and B)

Multiplication rule

The multiplication rule states that the probability of two or more independent events occurring together is the product of their individual probabilities.

P(A and B) = P(A) * P(B)

Conditional probability

Conditional probability is the probability of an event occurring, given that another event has occurred. It is represented as:

P(A|B) = P(A and B) / P(B)

Solving probability problems step-by-step

To solve a probability problem, you need to follow a step-by-step process. Here is a sample problem and how to solve it using the steps:

Problem: What is the probability of rolling a sum of 7 on two dice?

Step 1: Define the event.

The event is rolling a sum of 7 on two dice.

Step 2: Determine the sample space.

The sample space for rolling two dice is:

{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

Step 3: Determine the favourable outcomes.

The favourable outcomes for rolling a sum of 7 on two dice are:

{(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

Step 4: Calculate the probability.

The probability of rolling a sum of 7 on two dice is:

P(Sum of 7) = Number of favorable outcomes / Total number of possible outcomes             = 6 / 36             = 1 / 6             = 0.1667             = 16.67%

Tips for improving your probability skills

To improve your probability skills, here are some tips:

Practice, practice, practice

The more you practice, the better you get. Try to solve as many probability problems as you can, and review your mistakes to learn from them.

Understand the concepts

Make sure you understand the key concepts and terms of probability. If you don’t understand them, you won’t be able to solve the problems effectively.

Learn the formulas

Memorize the formulas for addition, multiplication, and conditional probability. They will be essential in solving problems quickly.

Use visual aids

Use visual aids like diagrams, tables, and charts to help you understand the problem better.

Probability resources and study materials

Here are some resources and study materials to help you improve your probability skills:

Online tutorials

There are many online tutorials available that can help you learn probability. Some of the best ones are Khan Academy, Math Is Fun and Brilliant.

Books

There are several books available on probability that can help you improve your skills. Some of the best ones are “Introduction to Probability” by Sheldon Ross, “Probability and Statistics” by Morris DeGroot, and “Probability Theory: The Logic of Science” by E.T. Jaynes.

Practice problems

There are many websites and books available that provide practice problems for probability. Some of the best websites are Math-Aids, Math-Drills, and MathWorksheetsLand. Some of the best books are “11+ Maths Practice Book With Assessment Tests” by CGP Books and “Bond 11+: Maths: Assessment Papers: 6-7 years” by Michellejoy Hughes.

Conclusion

Probability is an essential topic in the 11 Plus Math Exam, and mastering it can significantly impact your score. By understanding the key concepts, learning the formulas, and practicing regularly, you can improve your probability skills and tackle any problem with ease. Remember to use visual aids, review your mistakes, and seek help from resources and study materials. Good luck with your preparations!