 # 7.4.1 Probability II, SPM Paper 1 (Short Questions)

Question 1:
A bag contains 36 marbles which are black and white. It is given that the probability for a black marble being picked at random from the bag is $\frac{5}{9}$ .
Calculate the number of white marbles to be taken out from the bag so that the probability of picking a black marble is   $\frac{5}{8}$ .

Solution:

Question 2:
Table below shows the number of different coloured balls in three bags.

 Green Brown Purple Bag A 3 1 6 Bag B 5 3 4 Bag C 4 6 2
If a bag is picked at random and then a ball is drawn randomly from that bag, what is the probability that a purple ball is drawn?

Solution:

Probability of picking a bag = $\frac{1}{3}$
Probability of picking purple ball from bag A = $\frac{6}{10}=\frac{3}{5}$
Probability of picking purple ball from bag B = $\frac{4}{12}=\frac{1}{3}$
Probability of picking purple ball from bag C = $\frac{2}{12}=\frac{1}{6}$

$\begin{array}{l}P\left(\text{purple ball}\right)\text{=}\left(\frac{1}{3}×\frac{3}{5}\right)+\left(\frac{1}{3}×\frac{1}{3}\right)+\left(\frac{1}{3}×\frac{1}{6}\right)\\ \text{}=\frac{1}{5}+\frac{1}{9}+\frac{1}{18}\\ \text{}=\frac{11}{30}\end{array}$

Question 3:
A box contains 48 marbles. There are red marbles and green marbles. A marble is chosen at random from the box. The probability that a red marble is chosen is $\frac{1}{6}.$
How many red marbles need to be added to the box so that the probability that a red marble is chosen is  $\frac{1}{2}.$

Solution:

Question 4:
A box contains 5 red cards, 3 yellow cards and a number of green cards. A card is picked at random from the box. Given that the probability of picking a yellow card is $\frac{1}{6}$ , find the probability of picking a card that is not green.

Solution: