Everything Maths Grade 11

19.2 CHAPTER 19. INDEPENDENT AND DEPENDENT EVENTS

Step 1 : Identify the two events and determine whether the events are independent or

not

Event A is selecting a R 1 coin and event B is next selecting a R 2. Since the

outcome of the first event affects the outcome ofthe second event (because there

are less coins to choosefrom after the first coin has been selected), the events are

dependent.

Step 2 : Determine the probability of the specific outcomes occurring, for eachevent

The probability of first selecting a R 1 coin is^14 and the probability of next

selecting a R 2 coin is^23 (because after the R 1 coin has been selected, there are

only three coins to choose from).

Therefore, P(A) =^14 and P(B) =^23.

Step 3 : Use equation 19.1 todetermine the probability of the two events occurring

together.

The same equation as for independent events areused, but the probabilities

are calculated differently.

P(A∩ B) = P(A)× P(B)

=

1

4

×

2

3

=

2

12

=

1

6

The probability of first selecting a R 1 coin followed by selecting a R 2 coin is

1

6.

Identification of Independent and Depen-

dent Events

EMBEI

Use of a Contingency Table

A two-way contingencytable (studied in an earlier grade) can be used todetermine whether events are
independent or dependent.

DEFINITION: two-way contingency table

A two-way contingencytable is used to represent possible outcomes when two events

are combined in a statistical analysis.