**Question 9**:

Table 1 shows the name of four boys and a girl in SMK Pelangi who are assigned to raise the flag during the school assembly.

**Table 1**

Two pupils are chosen at random to raise the flag.

**(a)**List all the possible outcomes of the event for this sample space.

You may use the capital letter such as A for Adam and so on. [2 marks]

**(b)**

**By listing down all the possible outcomes of the event**, find the probability that

**(i)**the students chosen are of different gender,

**(ii)**Borhan and Daljit are not assigned together. [4 marks]

**Solution**:**(a)**

*A*= Adam,

*B*= Borhan,

*C*= Chan,

*D*= Daljit,

*E*= Elina

S = {

*AB*,

*AC*,

*AD*,

*AE*,

*BC*,

*BD*,

*BE*,

*CD*,

*CE*,

*DE*}

**(b)(i)**

{

*AE*,

*BE*,

*CE*,

*DE*}

$\begin{array}{l}\text{Probability}=\frac{4}{10}\\ \text{}=\frac{2}{5}\end{array}$

**(b)(ii)**

{

*BD*}

$\begin{array}{l}\text{Probability}=1-P\left(\text{BorhanandDaljit}\right)\\ \text{}=1-\frac{1}{10}\\ \text{}=\frac{9}{10}\end{array}$

**Question 10**:

Diagram 5 shows an oil tanker. The oil tank of the lorry is a cylindrical with 20 m length and 2.1 m in radius. The tank is half filled with oil.

**Diagram 5**

Upon arrival at a petrol station, all of the fuel in the tanker was pumped out equally into 2 cuboidal tanks, built underground.

Using $\pi =\frac{22}{7}$ , calculate the height, in m, of the oil level in the tank. [4 marks]

**Solution**:$\begin{array}{l}\frac{1}{2}\pi {r}^{2}t=2\times \text{Volumeofcuboid}\\ \frac{1}{2}\times \frac{22}{7}\times {2.1}^{2}\times 20=2\times \left(5\times 2\times \text{heightofcuboid}\right)\\ \text{}138.6=20\times \text{heightofcuboid}\\ \text{heightofcuboid}=6.93\text{m}\end{array}$