Tree diagrams, selection without replacement and repeated trials
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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
- Draw the future
- The two rules
- Without replacement
Read the transcript of the teaching part
Last time
Before we start: last time, in Conditional probability, independent events, enumeration and two-way tables, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Draw the future
A driving test you can retake, a bag you pick from twice, a coin that decides which bag. Each of these is a story with branching choices, and a tree diagram is a picture of that story. Once the tree is drawn, every question is the same two moves: multiply along a path, add across paths.
The two rules
Each branch carries a probability. The branches from one point add to one. To find the probability of a path, multiply the probabilities along it. To find the probability of an event that can happen in several ways, add the path probabilities.
Without replacement
When you pick without replacement, the numbers in the bag shrink. The second set of branches has a smaller denominator. Bag A has 5 red and 3 blue. The chance of red, then red is 5 over 8 times 4 over 7, which is 5 over 14. With replacement, the branches would repeat unchanged. Read the question for which one it is.
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.