Page 28 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

Example 30

A card is drawn randomly from a standard deck of 52 cards with replacement.
Determine whether the events “getting a spade” and “getting a numeric card” are independent.
Solution: Let event A = a spade is chosen,
event B = a numeric card is chosen.
P(B | A) = 40 = 10 and P(B) = 40 = 10 .
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Since P(B | A) = P(B), events A and B are independent.
2
Example 31

The table below shows 80 students registered for a programming course.
Basic Advanced
Girls 11 24
Boys 16 29
Determine whether the events “a girl is selected” and “a student register advanced programming is
selected” are independent.
Solution: Let event A be a girl is selected,
event B be a student register advanced programming is selected.

From the table, P(A) = 11 + 24
80
= 35
80
= 7
16
= 0.4375

and P(A | B) = P(A  B)
P(B)
24
80
=
24 + 29
80
= 24
53
= 0.4528
Since P(A | B) ≠ P(A), the two events are dependent.

Probability of the intersection of events
Based on the definition of the conditional probability we have

P(A  B) = P(A | B) × P(B)

This is called the multiplication rule of probability.

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