Modelling with probabilityEdexcel A-Level Maths: Mind map

Exam questions on Modelling with probability

1. 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
2. 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
3. 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