9.4.2 Probability of Combined Events, SPM Paper (Short Questions)

Question 5:
In an office, 300 workers go to work by bus, 60 workers go by car and the rest go by motorcycle. A worker is chosen at random. The probability of choosing a worker who goes to work by bus is ⅔.
Find the probability of choosing a worker who does not go to work by motorcycle.

Solution:
$\begin{array}{l}\text{Let }y\text{ be the number of workers who go to office by motorcycle}\text{.}\\ \text{P}\left(\text{by bus}\right)=\frac{2}{3}\\ \frac{\text{Number of workers }\left(\text{By bus}\right)}{\text{Total number of workers}}=\frac{2}{3}\\ \frac{300}{300+60+y}=\frac{2}{3}\\ 900=720+2y\\ 2y=180\\ y=90\\ \\ \text{Probability}=\frac{300+60}{360+90}\\ =\frac{360}{450}\\ =\frac{4}{5}\end{array}$

Question 6:
A box contains 18 black cards and 8 blue cards. Fanny puts another 2 black cards and 4 blue cards inside the box. A card is chosen at random from the box.
What is the probability that a black card is chosen?

Solution:
$\begin{array}{l}\text{New total number of cards in the box}\\ =\left(18+2\right)+\left(8+4\right)\\ =32\\ \\ \text{Probability a black card is chosen}\\ \text{Probability}=\frac{18+2}{32}\\ =\frac{20}{32}\\ =\frac{5}{8}\end{array}$

Question 7:
A fruits seller wants to check the number of rotten apples in each box. Table below shows the number of rotten apples in each box.
Given that there were 55 boxes of apples.
If a box is selected at random, what is the probability that the box does not contain rotten apples?

Solution:
$\begin{array}{l}\text{Number of boxes without rotten apples}\\ =55-\left(3+9+2+3+1+2\right)\\ =55-20\\ =35\\ \\ \text{Probability}=\frac{35}{55}=\frac{7}{11}\end{array}$

Question 8:
A form 5 science class has 15 boy students and a number of girl students. A student is chosen at random from the class. The probability of choosing a boy student is $\frac{3}{5}$ .
Find the number of girl students in the class.

Solution:
$\begin{array}{l}\text{Let }x\text{ be the number of girl students in the class}\text{.}\\ \text{P}\left(\text{a girl student}\right)=1-\frac{3}{5}\\ =\frac{2}{5}\\ \frac{x}{15+x}=\frac{2}{5}\\ 5x=30+2x\\ 3x=30\\ x=10\end{array}$