Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The table below lists how many boys and girls in a group of students study Art, Music and Drama. Every one of the $160$ students studies only one of these subjects. Boys: Art $24$, Music $40$, Drama $32$. Girls: Art $15$, Music $12$, Drama $37$.
(i)[1]
Find the probability that a student chosen at random is studying Music.
(ii)[2]
Determine whether the events ‘a randomly chosen student is a boy’ and ‘a randomly chosen student is studying Music’ are independent, and justify your answer.
(iii)[2]
Find the probability that a student chosen at random is not studying Drama, given that the student is a girl.
(iv)[5]
Three students are selected at random. Find the probability that exactly $1$ is studying Music and exactly $2$ are boys.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct probability is $52/160=13/40=0.325$.” …