6th Grade Math Textbook, Fundamentals

 &KDSWHU

12-6

Update your skills. See page 414 XVII.

Compound Events

Objective To find the probability of independent events

• To find the probability of dependent events

In a language arts class, 10 students must do individual oral
presentations. The class meets each day Monday through Friday.
The teacher determines that two presentations would be presented
each day. The teacher places cards in two jars. The first jar
determines the order of the presentations (first or second) on the
specific day. The second jar determines the day (Monday through
Friday) of the presentation. For each jar, the possibilities are
equally likely. Joy is the first student to choose from the jars.
What is the probability that Joy will present first on Friday?

To determine the probability of presenting first on Friday,
find the probability of the compound event.

A is an event that consists of two or more events

considered as a single event.

A compound event can be an independent eventor a dependent event.

For an , the occurrence of one event does notaffect

the probability or likelihood that the other event will occur. For a

, the occurrence of one event affects the probability

or likelihood that the other will occur.

Since Joy’s pick from jar 1 does not affect the pick from jar 2

and her pick from jar 2 does not affect the pick from jar 1, the

events are independent.

To find the probability of independent events,

multiply the probability of each event.

First identify the events.

Let event AJoy presenting first.

Let event B Joy presenting on Friday.

P(A and B) P(A) P(B)

P(firstand Friday) P(first) P(Friday)

   

The probability that Joy will present first on

Friday is or 0.1 or 10%.

Check:Draw a tree diagram to check your answer.

Sample space {(1st, M); (1st, T); (1st, W); (1st, Th);

(1st, F); (2nd, M); (2nd, T); (2nd, W);

(2nd, Th); (2nd, F)}

Using the sample space, you can confirm that the

probability of Joy presenting first on Friday is

, 0.1 or 10%.

dependent event

independent event

compound event

1

2

1

5

1

10

1

10

1

10

Key Concept

Probability of Independent Events

If A and B are independent events,

then P(A and B) P(A) P(B).

Event A Event B

Monday

Tuesday

Wednesday

Thursday

Friday

1 st

Monday

Tuesday

Wednesday

Thursday

Friday

2 nd