Probability distributions: by selection, from outcomes, and with unknowns
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 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
- List it, count it, check it
- Selecting coins
Read the transcript of the teaching part
Last time
Before we start: last time, in Tree diagrams, selection without replacement and repeated trials, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
List it, count it, check it
Building a probability distribution is bookkeeping. List every possible value of X, find how many ways each can happen, and divide by the total number of equally likely outcomes. Then the checks do the rest: the probabilities must sum to one, and once the table is right, the mean and variance follow from two sums.
Selecting coins
Jasmine has one 5 dollar coin, two 2 dollar coins and two 1 dollar coins. She picks two. There are 5 choose 2, which is 10, equally likely selections. A total of 7 needs the 5 and a 2. The 5 is paired with either 2 dollar coin: 2 ways out of 10, which is 0.2. List all totals: 2 happens once, 3 happens 4 times, 4 once, 6 twice, 7 twice. That gives 0.1, 0.4, 0.1, 0.2, 0.2.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Finding an unknown value · Probability distribution by selection · Probability distribution from outcomes · Unknown probabilities in a table.
The whole chapter: Discrete Random Variables, Probability, The Normal Distribution.
Chapter 5.4: Discrete random variables
- Probability distributions: by selection, from outcomes, and with unknowns 6 min
- The binomial and normal distributions 6 min
- Binomial and geometric distributions, and drawing a probability distribution 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.