 # 7.4.1 Probability 1, Paper 1 (Short Questions)

Question 1:
A box contains 5 pink marbles and 21 yellow marbles. Sharon puts another 4 pink marbles and 1 yellow marble inside the box. A marble is chosen at random from the box.
What is the probability that a pink marble is chosen?

Solution:

Total number of pink marbles = 5 + 4 = 9
Total number of yellow marbles = 21 + 1 = 22
Total number of marbles = 9 + 22 = 31

$\therefore P\left(\text{pink marble}\right)=\frac{9}{31}$

Question 2:
In a group of 80 prefects, 25 are girls. Then 10 boys leave the group.
If a prefect is chosen at random from the group, state the probability that the prefect chosen is a boy.

Solution:

Number of boys = 80 – 25 = 55

After 10 boys left,
Number of boys = 55 – 10 = 45

Total number of prefects = 25 + 45 = 70
$\therefore P\left(boy\right)=\frac{45}{70}=\frac{9}{14}$

Question 3:
60 people have taken part in a singing contest. If a person is chosen at random from all the contestants, the probability of getting a male contestant is $\frac{8}{15}$ . If there are 12 males and 3 females who did not qualify to the second round, find the probability that a male is chosen from the second round contestants.

Solution:
Number of male contestants = 60 × $\frac{8}{15}$ = 32

After 12 males and 3 females left,
Total number of contestants left = 60 – 15 = 45

Number of male contestant = 32 – 12 = 20
$\therefore P\left(\text{male contestant}\right)=\frac{20}{45}=\frac{4}{9}$

Question 4:
John has a collection of stamps from Thailand, Indonesia and Singapore. He picks one stamp at random. The probability of picking a Thailand stamp is $\frac{1}{5}$  and the probability of picking an Indonesia stamp is $\frac{8}{15}.$  John has 20 Singapore stamps. Calculate the total number of stamps in his collection.

Solution:

$\begin{array}{l}\text{Probability of picking a Singapore stamp}\\ =1-\frac{1}{5}-\frac{8}{15}\\ =\frac{4}{15}\\ \\ \text{Given that John has 20 Singapore stamps,}\\ \therefore \text{Total number of stamp in John's collection}\\ =\frac{15}{4}×20\\ =75\end{array}$