Binomial and geometric distributions, and drawing a probability distribution
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Waiting, or counting?
- Geometric distribution
- A worked example
Read the transcript of the teaching part
Last time
Before we start: last time, in The binomial and normal distributions, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Waiting, or counting?
Throw a die until a six appears. Or throw it ten times and count the sixes. They look alike, but one asks how long you wait, and the other asks how many successes in a fixed number of tries. Choosing between geometric and binomial is the whole skill. After that, the formulas are short.
Geometric distribution
Each trial has success probability p, independent. X is the number of the trial on which the first success happens. To succeed on trial r, you need r minus 1 failures, then a success: P of X equals r is q to the r minus 1, times p. At least r trials needed means r minus 1 failures: P of X at least r is q to the r minus 1.
A worked example
A fair die is thrown until a 4 appears. The probability of a 4 is one sixth. P of fewer than 6 throws is 1 minus P of 6 or more. P of 6 or more is the probability that the first 5 throws all fail: five sixths to the 5. So P of fewer than 6 is 1 minus five sixths to the 5, which is 4651 over 7776, about 0.598.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Binomial and geometric distributions · Drawing a probability distribution · Geometric distribution.
The whole chapter: Discrete Random Variables, Probability.
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.