Everything Maths Grade 11

CHAPTER 19. INDEPENDENT AND DEPENDENT EVENTS 19.2

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

not

Event A is rolling a 1 and event B is rolling a 6. Since the outcome ofthe

first event does not affect the outcome of the second event, the events are inde-

pendent.

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

The probability of rolling a 1 is^16 and the probability of rolling a 6 is^16.

Therefore, P(A) =^16 and P(B) =^16.

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

together.

P(A∩ B) = P(A)× P(B)

=

1

6

×

1

6

=

1

36

The probability of rolling a 1 and then rolling a 6 on a fair die is 361.

Consequently, two events are dependent if theoutcome of the first event affects the outcome of the
second event.

DEFINITION: Dependent events

Two events are dependent if the outcome of oneevent is affected by theoutcome of

the other event i.e. P(A/C)�= P(A).

Example 2: Dependent Events

QUESTION

A cloth bag has four coins, one R 1 coin, two R 2 coins and one R 5 coin. What is the probability

of first selecting a R 1 coin and then selectinga R 2 coin?

SOLUTION