Probability
Probability is the branch of Maths that uses numbers to describe how likely something is to happen. Probability is the study of the chance or likelihood of an event happening.
KEY POINTS ABOUT PROBABILITY.
1. Probability is measured on a scale from zero to one, i.e. 0 ≤ P(E) ≤ 1. The probability of an impossibility is zero and the probability of a certainty is one. Probabilities always add up to 1. 2. The probability formula:
3. You can also calculate the probability of an event not happening using the formula below: P(not E)=1 – P(E).
4. Sample space: The set of all possible outcomes is called a sample space. Example: The sample space when throwing a dice is {1,2,3,4,5,6}. 5. Experimental probability: 6. Mutually exclusive events: Events are
mutually exclusive if they cannot occur at the same time.
7. Independent events: Two events are independent if the outcome of one event does not affect the outcome of another. 8. Dependent events: Events are dependent on each other if the outcome of one affects the outcome of another.
9. The addition rule (The OR Rule): When two events, A and B, are mutually exclusive then
P(A or B)= P(A)+P(B).
When two events, A and B, are not mutually exclusive,
P(A or B) = P(A)+P(B)-P(A and B).
10. The multiplication rule (The AND Rule): P(A and B) = P(A)×P(B).
11. Bernoulli trials: Bernoulli trials have two outcomes; success and failure.
12. Probability and Venn diagrams: There is nothing particularly new about this section. The main difference is that the information for the question is presented using Venn diagrams. Make sure that you are familiar
with the terminology involved with sets/ Venn diagrams.
13. Probability and tree diagrams: Tree diagrams can also be used to display possible outcomes of events. They can be used to show both independent and dependent events. The branches of the tree diagram represent the probabilities. Each pair of branches needs to add up to one, since the sum of probabilities add up to one.
14. Expected value: The expected value is also known as the average outcome of an experiment. The formula to work out the expected value is
E(x )=∑ xP(x)
This means we must add up the values of each outcome multiplied by the probability of getting that outcome.
15. Fundamental principle of counting: Suppose one operation has m possible outcomes and a different operation has n possible outcomes. The number of possible outcomes when performing the first operation followed by the second operation is m×n.
16. Permutations\arrangements: When you are asked about the number of permutations, you are being asked about the number of possible arrangements of events. Three objects can be arranged in 3! ways (pronounced factorial), i.e.
3!=3×2×1=6 ways.