Section 4-6 Probability of Compound EventsSPI 53B: Compute the probability of a simple compound event

Objective: • Compute the probability of a simple compound event (both independent and dependent).

Probability: • how likely something is to occur• must be between 0 and 1• we computed one simple event

Independent events: • events that do not influence one another

Dependent events: • events that influence each other

• Events that do not influence one another• like rolling a red and black number cube

• Selecting with replacement• Written as: P(A and B) = P(A) ∙ P(B)• “And” means to multiply

Independent Events

Suppose you roll a red cube and a black cube. What is the probability that you will roll a 3 on the red and an even on the black?

P(red 3 and black even) =

P(roll a 3 on red cube) = P(roll even on black) =6

1

2

1

6

3

12

1

2

1

6

1

In a word game, you choose a tile from a bag containing the letters shown:

A L G E B R A I S C O O L

Dependent Events

• Events that influence each other • Occurrence of one affects the probability of the other• Written as P(A then B) = P(A) ∙ P(B after A)

There is a total of 13 choices, so… P(select an A) =

Without replacing the tile, you select a second tile. What is the probability you will select an A then an L?

1st Selection

The probability of the dependent events is:

2d Selection

There is a total of 12 tiles for the 2d selection, so … P(L after A) = 13

2

6

1

12

2

39

1

6

1

13

2

Suppose you roll 2 cubes. What is the probability that you will roll an odd number on the first cube and a multiple of 3 on the second cube?

P(odd and multiple of 3) = P(odd) • P(multiple of 3)

P(odd) = =36

12

There are 3 odd numbers out of six numbers.

P(multiple of 3) = =26

13

There are 2 multiples of 3 out of the 6 numbers.

= •12

13

= 16

Substitute.

Simplify.

Probability

Is the event dependent or independent? INDEPENDENT

Suppose you have 3 quarters and 5 dimes in your

pocket. You take out one coin, and then put it back. Then

you take out another coin. What is the probability that you

take out a dime and then a quarter?

Since you replace the first coin, the events are independent.

P(dime and quarter) = P(dime) • P(quarter)

= • =58

38

1564

P(dime) = There are 5 out of 8 coins that are dimes.58

P(quarter) = There are 3 out of 8 coins that are quarters.

38

Probability

Is the event dependent or independent? INDEPENDENT

A teacher must select 2 students for a conference.

The teacher randomly picks names from among 3 freshmen,

2 sophomores, 4 juniors, and 4 seniors. What is the

probability that a junior and then a senior are chosen?

P(junior) = There are 4 juniors among 13 students413

P(senior after junior) = There are 4 seniors among 12 remaining students.

412

P(junior then senior) = P(junior) • P(senior after junior)

= • = 4

134

124

39

Probability

Since you do not replace the first person chosen, the events are dependent.

Is the event dependent or independent? DEPENDENT