7.3 Probability of an Event

(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.

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
P ( A ) = n ( A ) n ( S ) = 24 80 = 3 10


(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 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 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
n ( W ) = P ( W ) × n ( S ) = 2 5 × 30 = 12

(b)

Given n(R) = 8
n(B) = 30 – 12 – 8 = 10
P ( B ) = n ( B ) n ( S ) = 10 30 = 1 3

Leave a Reply

Your email address will not be published. Required fields are marked *