Download ProbabilityofCompoundEventsNotes

Probabilities of Compound Events!
We will be discussing independent events, dependent events, and mutually exclusive events!
First, we must know what makes events independent…
Independent Events: Events that are ______ affected by one another!
2 Examples:
- Rolling a _____ and then choosing a _______.
- Choosing a marble from a bag, _______________ it, and then choosing again.
What is the probability of choosing an Ace from a deck of cards and then rolling an odd number
on a 6-sided die?
Long Way
Shortcut!
How many Aces are there? ____
How many odds on a die? ____
*How many Ace/odd outcomes? __________
How many cards exist? ____
How many numbers on a die? ____
*How many possible outcomes? ______________
Probability of choosing an Ace? ___
Probability of rolling an odd? ___
Probability of choosing an Ace and
then rolling an odd:
Probability:
Whether events are independent or dependent, we can ________________ their probabilities!
Symbols: P(A and B) = _________________
In a bag, there are 6 green marbles, 5 blue, 8 yellow, and 1 black. We are going to pick a
marble, replace that marble, and then pick again! Find the following probabilities…
P(green then yellow)
P(black then green)
P(2 blue in a row)
P(2 yellow in a row)
Dependent Events: Events that ______ affected by one another!
Example:
- Choosing a card, ____________________ it, and then choosing another!
In a bag, there are 6 green marbles, 5 blue, 8 yellow, and 1 black. We are going to pick a
marble, NOT replace that marble, and then pick again! Find the following probabilities…
Example: P(2 green in a row):
Numerator = At first there are ____ green
Denominator = At first there are ____ marbles total
After the marble is picked and NOT REPLACED
Numerator = Now there are _____ green
Denominator = Now there are ______ marbles total
So, P(2 green in a row) = _____________________________________________
P(green then yellow)
P(black then green)
P(2 blue in a row)
P(2 yellow in a row)
Mutually Exclusive Events: One event happening, ____ another event happening!
Example:
Rolling a die and getting a __________________.
For mutually exclusive events, we simply _____ their probabilities!
Symbols: P(A or B) = _________________
Now we will practice these types of events with our groups. Complete the worksheet #1-10
Probabilities of Compound Events
ANSWER KEY
We will be discussing independent events, dependent events, and mutually exclusive events!
First, we must know what makes events independent…
Independent Events: Events that are NOT affected by one another!
2 Examples:
Rolling a DIE and then choosing a CARD
Choosing a marble from a bag; REPLACING it, and then choosing again.
What is the probability of choosing an Ace from a deck of cards and then rolling an odd number
on a 6-sided die?
Long Way
Shortcut!
How many Aces are there? 4
How many odds on a die? 3
*How many Ace/odd outcomes? 4 x 3 = 12
How many cards exist? 52
How many numbers on a die? 6
*How many possible outcomes? 52 x 6 = 312
Probability of choosing an Ace 4/52
Probability of rolling an odd? 3/6
Probability of choosing an Ace and
then rolling an odd: 4/52 x 3/6
12/312 = 1/26
.0385 = 3.85%
Probability: 12/312 = 1/26 .0385 = 3.85%
Whether events are independent or dependent, we can MULTIPLY their probabilities!
Symbols: P(A and B) = P(A) x P(B)
In a bag, there are 6 green marbles, 5 blue, 8 yellow, and 1 black. We are going to pick a
marble, replace that marble, and then pick again! Find the following probabilities…
P(green then yellow)
6/20 x 8/20 = 48/400 = 3/25
.12 = 12%
P(black then green)
1/20 x 6/20 = 6/400 = 3/200
.015 = 1.5%
P(2 blue in a row)
5/20 x 5/20 = 25/400 = 1/16
P(2 yellow in a row)
8/20 x 8/20 = 64/400 = 4/25
.0625 = 6.25%
.16 =16%
Dependent Events: Events that ARE affected by one another!
Example:
Choosing a card, NOT REPLACING it, and then choosing another!
In a bag, there are 6 green marbles, 5 blue, 8 yellow, and 1 black. We are going to pick a
marble, NOT replace that marble, and then pick again! Find the following probabilities…
Example: P(2 green in a row):
Numerator = At first there are 6 green
Denominator = At first there are 20 marbles total
After the marble is picked and NOT REPLACED
Numerator = Now there are 5 green
Denominator = Now there are 19 marbles total
So, P(2 green in a row) = 6/20 x 5/19 = 30/380 = 3/38 .0789 = 7.89%
P(green then yellow)
6/20 x 8/19 = 48/380 = 12/95
.126 = 12.6%
P(black then green)
1/20 x 6/19 = 6/380 = 3/190
.0158 = 1.58%
P(2 blue in a row)
5/20 x 4/19 = 20/380 = 1/19
.0526 = 5.26%
P(2 yellow in a row)
8/20 x 7/19 = 56/380 = 14/95
.147 = 14.7%
Mutually Exclusive Events: One event happening, OR another event happening!
Example:
Rolling a die and getting a 1 or a 2
For mutually exclusive events, we simply ADD their probabilities!
Symbols: P(A or B) = P(A) + P(B)