Page 23 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

Example 25

Consider the experiment of selecting one card at random from a standard deck of 52 playing cards. Find
the probability of drawing either a king or a diamond card.
Solution: Let event A = a king card is drawn,
event B = a diamond card is drawn.
As there are 4 king cards in the deck, P(A) = 4 = 1 ,
52 13
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and the deck has 13 diamond cards, so P(B) = 13 = 1 .
52 4
Since there is 1 card corresponding the king of diamond, P(A  B) = 1 . 2
52
By applying the formula, P(A  B) = P(A) + P(B) – P(A  B), we have
P(A  B) = 1 + 1 – 1
13 4 52
= 4
13
The probability of drawing either a king or a diamond card is 4 .
13

Relative frequency data for two or more events is often summarised in a table called a contingency table.
We can easily determine probabilities from this table.

Example 26

A survey of 150 students on their reading habit over the weekend is presented in the contingency table.
Newspaper Total
Yes No
Yes 16 21 37
Magazine
No 75 38 113
Total 91 59 150
If a student under the survey is selected at random, find the probability that the student reads newspaper
or reads a magazine.
Solution: Let A be the event that the student selected reads newspaper,
B be the event that the student selected reads a magazine.

From the table, there are 91 students out of a total of 150 students reading
newspapers,
hence P(A) = 91 .
150
There are 37 students out of a total of 150 students reading magazine, hence
37
P(B) = 150 .
The probability that the selected student reads both newspaper and a magazine,
16
P(A  B) = 150 .

91

02 STPM Math(T) T3.indd 91 28/10/2021 10:21 AM