(A) Probability of an Event
1. The probability of an event A, P(A) is given by
2. If P(A) = 0, then the event A will certainly not occur.
3. If P(A) = 1, then the event A will certainly to occur.2. If P(A) = 0, then the event A will certainly not occur.
Example 1:
Table below shows the distribution of a group of 80 pupils playing a game.
Form Four

Form Five


Girls

28

16

Boys

12

24

A pupil is chosen at random from the group to start the game.
What is the probability that a boy from Form Five will be chosen?
Solution:
Let
A = Event that a boy from Form Five
S = Sample space
n(S) = 28 + 12 + 16+ 24 = 80
n(A) = 24
$\begin{array}{l}P(A)=\frac{n(A)}{n(S)}\\ \text{}=\frac{24}{80}=\frac{3}{10}\end{array}$
(B) Expected Number of Times an Event will Occur
If the probability of an event A and the number of trials are given, then the number of times event A occurs
= P(A) × Number of trials
Example 2:
In a football training session, the probability that Ahmad scores a goal in a trial is ⅝. In 40 trials are chosen randomly, how many times is Ahmad expected to score a goal?
Solution:
Number of times Ahmad is expected to score a goal
= ⅝ × 40
= 25
(C) Solving Problems
Example 3:
Kelvin has 30 white, blue and red handkerchiefs. If a handkerchief is picked at random, the probability of picking a white handkerchief is
$\frac{2}{5}.$
Calculate
(a) the number of white handkerchiefs.
(b) the probability of picking a blue handkerchief if 8 of the handkerchiefs are red in colour.
Solution:
Let
W = Event that a white handkerchief is picked.
B = Event that a blue handkerchief is picked.
R = Event that a red handkerchief is picked.
S = Sample space
(a)
n(S) = 30
$\begin{array}{l}n(W)=P(W)\times n(S)\\ \text{}=\frac{2}{5}\times 30=12\end{array}$
(b)
Given n(R) = 8
n(B) = 30 – 12 – 8 = 10
$\begin{array}{l}P(B)=\frac{n(B)}{n(S)}\\ \text{}=\frac{10}{30}=\frac{1}{3}\end{array}$
$\begin{array}{l}P(B)=\frac{n(B)}{n(S)}\\ \text{}=\frac{10}{30}=\frac{1}{3}\end{array}$