Name:
__________________________________
Date: ___________________
Integrated Advanced Algebra
Notes: Compound Probability
Textbook: Lesson 6.4, Pages 351 – 354
Homework: Compound Probability Worksheet
Period:
_________
Probability is a number from 0 to 1 indicating the likelihood of an event.
There are two kinds of probability: experimental and theoretical.
Theoretical probability can be found by dividing the number of outcomes of
an event by the total number of all possible outcomes. This is only
possible when all outcomes are known. When the outcome possibilities are
not known, then the results of an experiment are used to find the
experimental probability.
number of outcomes of event A
Probability of event A happening = P(A) =
total number of all possible outcomes
Example 1: A bag contains 6 red marbles.
bag.
a. What is the probability it is red?
probability it is blue?
You draw out a marble from the
b.
What is the
When an event is guaranteed to happen, its probability of occurring is
___________.
When an event is guaranteed not to happen, its probability of occurring is
___________.
Events are called mutually exclusive when the events cannot all happen at
the same time, such as rolling a 6-sided die and getting 1 or 3. The
probability of one of the mutually exclusive events happening can be found
by adding together the probabilities of each event happening.
P(A or B) = ___________ + ___________
Example 2: You roll a cube with sides numbered 1 to 6. Find the
probability that …
a. … you roll 1 or 3.
b. … you roll 4, 5, or 6?
Example 3: A jar contains 14 red, 9 black, and 7 white marbles.
marble is drawn at random, find the indicated probability.
a. P (red or black)
b. P (black or white)
If a
But what if we want more than one event to happen? Then, we must first
determine if the events are independent or dependent on each other. Events
are independent when the outcome of one event does not affect the outcome
of the second (or subsequent) events, such as rolling a 6-sided die and
getting first 5 and then 2. Events are dependent when the outcome of the
first event affects the probability of the second event, such as drawing a
Name:
__________________________________
Date: ___________________
Period: _________
marble from a bag and then drawing another without returning the first
marble to the bag.
Example 4: Determine whether the following events are independent or
dependent.
a. Flipping a coin for heads and
b. Drawing a spade from a deck,
spinning a game spinner for
keeping it, then drawing a heart
$500.
from the deck.
The probability of two independent events both happening can be found by
multiplying the probabilities of each event happening.
P (A and B) = ___________ * ___________
The probability of two dependent events both happening can be found by
multiplying the probability of the first event happening times the
probability of the second event happening after the first event occurs.
P (A and B) = ___________ * _____________________________
Example 5: Twice, you roll a die with sides numbered 1 to 10. Find the
probability that …
a. … you roll 5, then 7.
b. … you roll an even,
then an odd.
Example 6: Two cards are drawn from a standard playing deck of 52 cards,
without replacement. Find the probability that …
a. … both cards are kings.
b. … the first is a club and the
second a heart.
Example 7: A jar contains 8 green, 10 blue, and 2 orange marbles. If the
marbles are removed and not replaced, find the indicated probability.
a. P (green and then blue)
b. P (orange, then orange, and
then green)
$300
$500
$600
Example 8: The game spinner below has eight
congruent sections. If the arrow is spun
twice, find the indicated probability of the
first event and then the second event
occurring.
a.
$800
$100
$200
$700
$400
P ($100 and then $800)
Name:
__________________________________
Date: ___________________
b.
P (greater than $400 and then greater than $600)
c.
P (less than $800 and then less than $200)
d.
Period:
_________
P (two spins have a sum of $800)