Download Probability of Compound Events

PROBABILITY
OF COMPOUND
COMPOUND EVENTS
Made up of two or more events.
Example: the probability that a flight will
be on time & your luggage will arrive.
Create your own compound event.
INDEPENDENT EVENTS
The outcome of one event does NOT affect the outcome of the other.
Equation: P(A and B) = P(A) x P(B)
Symbol A n B
Example 1 : A bag contains 6 black marbles, 9 blue marbles, 4
yellow marbles, and 2 green marbles. A marble is selected, replaced,
and a second marble is selected. Find the probability of selecting a
black marble, then a yellow marble.
Example 2: P(blue, green)
Example 3: P(not black, blue)
DEPENDENT EVENTS
The outcome of one event affects the outcome of another event.
Equation: P(A and B) = P(A) x P(B following A)
Example 4 : A bag contains 6 black marbles, 9 blue marbles,
4 yellow marbles, and 2 green marbles. A marble is selected,
then a second marble is selected. Find the probability of
selecting a black marble, then a yellow marble.
Example 5: P(blue, green)
Example 6: P(not black or blue, blue)
COMPLEMENT OF A SET
The set of all objects that do NOT belong to the given set.
Example: The probability of drawing a heart & the
probability of NOT drawing a heart.
Create your own complement.
The sum of these probabilities is ALWAYS 1 whole or
100%.
CARDS
Total number of cards in a deck? ______
How many suits? _____ Name them.
How many cards are in each suit? _____
How many cards of each face? _____
How many different face cards? Name them.
How many of each color? _____
MUTUALLY EXCLUSIVE EVENTS
Events that can NOT occur at the same time.
Example: the probability of drawing a heart or a diamond.
Equation: P(A or B) = P(A) + P(B)
Symbol A u B
Example 7: A die is being rolled. Find the probability of rolling a 3
or 5.
Example 8: P(at least 4)
Example 9: P(less than 3)
NOT MUTUALLY EXCLUSIVE
Events that CAN occur at the same time.
Example: the probability of being on the honor roll, in the SADD club,
or being both on the honor roll & in the club.
Equation: P(A or B) = P(A) + P(B) – P(A and B)
Example 10: Of 240 girls, 176 are on the Honor Roll, 48 play sports,
and 36 are on the Honor Roll and play sports. What is the
probability that a randomly selected student plays sports or is on the
Honor Roll?
Example 11: Out of 5200 households surveyed, 2107 had a dog,
807 had a cat, and 303 had both a dog and a cat. What is the
probability that a randomly selected household has a dog or a cat?
REVIEW
Draw a model to describe the following terms. Define
each: Mutually Exclusive, Independent, Compound Events,
Not Mutually Exclusive, & Dependent.
CIRCLE THE SAMPLE SPACE
1.
What is the proportion of students who live in Currituck & are
male?
2.
What is the probability that a male student who passes Math II is
also in the SADD Club?
NAME THREE DIFFERENT PROBABILITY
MODELS…
1.
2.
3.
4.