The table below shows the number of male and female students studying Chemistry, Physics and Biology

Question

The table below shows the number of male and female students studying Chemistry, Physics and Biology at a private school.

	Chemistry	Physics	Biology
Male	$200$	$130$	$70$
Female	$250$	$300$	$50$

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

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.

One of the students selected at random is an international student. What is the probability that this student studies Chemistry?[2]
Three students are chosen at random. Find the probability that there is exactly one international student who studies Physics.[2]

Accepted Answer

(i) $\frac12$ (ii) $\frac{13}{20}$ (iii) $\frac{11}{20}$ $C$ and $M$ are not independent (iv) $\frac25$ (v) $0.294$

	Chemistry	Physics	Biology
Male	\(200\)	\(130\)	\(70\)
Female	\(250\)	\(300\)	\(50\)

2016 JJC P2 Q6