Modelling with probabilityAQA A-Level Maths: Flashcards
What these 13 flashcards ask
- What is a probability model?
- Name two common assumptions in probability models.
- When does the independence assumption fail?
- Effect of positive association on 'all events occur'?
- When does replacement matter?
- Why is the with-replacement model reasonable for a large population?
- Probability that none of 3 independent buses is late, each late with probability 0.15?
- Probability that exactly one of 3 is late, each with probability 0.15?
- Why multiply by 3 for 'exactly one of three'?
- How do you critique an assumption?
- What is a refinement of a model?
- What is the trade-off in refining a model?
- What should an assumption statement include?
Exam questions on Modelling with probability
- A school with 600 students models each student as absent on a given day with probability , independently of every other student.Suggest one change that would make the model more realistic, and give a reason.2 marks
- A bus company assumes that each bus on a route is late with probability , independently of the other buses. Three buses run on the route in the morning.A road closure delays every bus on the route. Explain why this makes the independence assumption unrealistic, and say how the true probability that all three buses are late compares with .2 marks
- A bag contains 10 counters, 4 red and 6 blue. A student wants the probability that two counters taken at random from the bag are both red, and models the draw as if the first counter were replaced before the second is taken. In fact the first counter is not replaced.Find the probability that both counters are red (i) using the student's model, (ii) using the actual procedure.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).