2016 JJC P2 Q6
The table below shows the number of male and female students studying Chemistry, Physics and Biology at a private school.
One of the students is chosen at random. Events $C$, $B$ and $M$ are defined as follows:
$C$ : The student chosen is studying Chemistry.
$B$ : The student chosen is studying Biology.
$M$ : The student chosen is a male.
Find
(i)
$\text{P}\left( C|M \right)$,
[1]
(ii)
$\text{P}\left( M\cup C \right)$,
[1]
(iii)
$\text{P}\left( M’\cap B’ \right)$.
[1]
Determine whether $C$ and $M$ are independent.
[2]
It is given that $20\%$ of Chemistry students, $30\%$ of Physics students and $5\%$ of Biology students are international students.
(iv)
One of the students selected at random is an international student. What is the probability that this student studies Chemistry?
[2]
(v)
Three students are chosen at random. Find the probability that there is exactly one international student who studies Physics.
[2]
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