Conditional probability, independent events, enumeration and two-way tables
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Probability with extra information
- Conditional probability
- Reading a two-way table
Read the transcript of the teaching part
Last time
Before we start: last time, in Arranging people in a line, and forming codes and numbers, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Probability with extra information
The chance that a randomly chosen student plays netball is one thing. The chance that a student plays netball, given that they are in Year 1, is another. Extra information shrinks the world you are choosing from. That one idea, conditional probability, powers two-way tables, independence tests and tree diagrams.
Conditional probability
The probability of A given B is the probability of both, divided by the probability of B. In words: restrict attention to the outcomes in B, then ask what fraction are also in A. The order matters. P of A given B is not the same as P of B given A.
Reading a two-way table
In a two-way table, the probability of a combination is the cell divided by the grand total. The probability of one category is its row or column total divided by the grand total. For a given condition, use the total of that row or column as the denominator. Do not use the grand total.
How often it comes up
The whole chapter: Probability.
Chapter 5.3: Probability
- Conditional probability, independent events, enumeration and two-way tables 6 min
- Tree diagrams, selection without replacement and repeated trials 6 min
Also for A Level Maths 9709 Paper 5
Which topics come up most in A Level Maths 9709 Paper 5 past papers, counted from every paper since 2004.