CIE A Level Maths: Probability & Statistics 1复习笔记2.3.1 Set Notation & Conditional Probability

What is set notation?

• Set notation is a formal way of writing groups of numbers (or other mathematical entities such as shapes) that share a common feature – each number in a set is called an element of the set

How do I solve problems given in set notation?

• Venn diagrams lend themselves particularly well to deducing which sets or parts of sets are involved- draw mini-Venn diagrams and shade them

• Practice shading various parts of Venn diagrams and then writing what you have shaded in set notation
• With combinations of union, intersection and complement there may be more than one way to write the set required
  • 
    Not convinced?  Sketch a Venn diagram and shade it in!
  • In such questions it can be the unshaded part that represents the solution

What is conditional probability?

• You have already been using conditional probability in Tree Diagrams
  • Probabilities change depending on the outcome of a prior event

• Consider the following example

• Tree diagrams are great for events that follow on from one another
  • • Otherwise Venn diagrams are extremely useful
      Beware! The denominator of fractional probabilities will no longer be the total of all the frequencies or probabilities shown
    • “given that” questions usually reduce the sample space as an event (a subset of the outcomes of the first experiment) has already occurred

What are two-way tables?

• In probability, two-way tables list the frequencies for the outcomes of two events – one event along the top (columns), one event down the side (rows)
• The frequencies, along with a “Total” row and “Total” column instantly show the values involved in finding probabilities

How do I solve problems given involving two-way tables?

• Questions will usually be wordy – and may not even mention two-way tables