(a) Explain briefly why statistical models are used when attempting to solve real-world problems.
(b) Write down the name of the distribution you would recommend as a suitable model for each of the following situations.
The weight of marmalade in a jar.
The number on the uppermost face of a fair die after it has been rolled.
(2)
There are 125 sixth-form students in a college, of whom 60 are studying only arts subjects, 40 only science subjects and the rest a mixture of both.
Three students are selected at random, without replacement.
Find the probability that
(a) all three students are studying only arts subjects,
(b) exactly one of the three students is studying only science subjects.