Modelling with probabilityEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

What is a probability model?
What does 'fair' mean for a die?
What are three common modelling assumptions?
How do you critique an assumption?
Give a reason independence may fail for buses.
Conditions for X\sim B(n,p)?
Binomial probability formula?
What must the probabilities of a valid discrete model add to?
Fair die rolled 60 times: expected sixes?
Observed 18 sixes in 60 rolls of a die: comment?
If P(result or more extreme) is large, what do you conclude?
Why might a small sample not settle a question about a model?
If p of lateness rises above 0.1, what happens to P(all 3 buses on time)?

Exam questions on Modelling with probability

A fair six-sided die is rolled twice. A student models the situation by assuming that the two rolls are independent and that each face is equally likely on each roll.
The die is rolled 60 times and a six occurs 18 times. Comment on the assumption that the die is fair.2 marks
A bus company models each of its buses as being late with probability $0.1$ , independently of every other bus. Three buses run on a route each morning.
At rush hour, the true probability that each bus is late is greater than $0.1$ . State the effect on the probability that all three buses are on time, and justify your answer.2 marks
The number of goals $X$ scored by a football team in a match is modelled by $P(X=0)=0.2$ , $P(X=1)=0.35$ , $P(X=2)=0.25$ , $P(X=3)=0.15$ and $P(X=4)=k$ , with no other values possible.
Find the value of $k$ and the probability that the team scores at least 2 goals.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).