Analytical Geometry
Name____________________
Applications of Probability Study Guide
Use the word bank to fill in the blanks.
Conditional Probabilities
Sample Space
Complement
Intersection
Two Way Frequency Tables
Union
Event
Mutually Exclusive
Independent
1. In probability, a _____________________ is the set of all possible
outcomes.
2. If the outcome of one event does not rely on the other event, the events
are _________________________.
3. The ___________________ of two or more events is all of the outcomes
shared by both events. It is denoted by the word “and” or with the symbol
.
4. Any subset from the sample space is an ________________________.
5. If the outcome of one event relies on the other event, the events are
_________________________________.
6. The _______________ of two or more events is all of the outcomes for
either event. It is denoted by the word “or” or the symbol .
7. The _____________________ of an event is the set of outcomes in the
same sample space that are not included in the outcomes of the event. It is
denoted by the word “not” or with the symbol ‘.
8. Two events are _____________________________ if the events cannot
occur at the same time.
9. _____________________________________ are found when one event
has already occurred and a second event is being analyzed. It is denoted
𝑃(𝐴|𝐵), and read “probability of A given B”.
Use color pencils to shade the appropriate parts of each Venn diagram using
the given notation.
1. 𝑃(𝐴 ∪ 𝐵)
2. 𝑃(𝐴 ∩ 𝐵)
3. 𝑃(𝐴′)
Identify the formula that matches with the correct type of event.
1. Mutually Exclusive Events
a. 𝑃(𝐴𝑎𝑛𝑑𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵)
2. Overlapping Events
b. 𝑃((𝐴|𝐵)) =
3. Conditional Probabilities
4. Independent Events
𝑃(𝐴∩𝐵)
𝑃(𝐵)
c. 𝑃(𝐴𝑜𝑟𝐵) = 𝑃(𝐴) + 𝑃(𝐵)
d. 𝑃(𝐴𝑜𝑟𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)
Practice Problems
1. Use the table to determine the probability of selecting a card that is a
heart, given that the card is a face card.
Define Event A_____________________
Define Event B_____________________
Write the notation__________________
Answer to question_________________
2. In Mr. Noland’s class, there are 12 boys and 16 girls. On Monday 4 boys
and 5 girls were wearing white shirts. What is the probability of
choosing a boy or a student wearing a white shirt?
Define Event A_____________________
Define Event B_____________________
Write the notation__________________
Answer____________________
3. Terry has a number cube with sides labeled 1 through 6. He rolls the
number twice. What is the probability that the sum of the two rolls is a
prime number, given that one of the rolls is a 3?
Define Event A_____________________
Define Event B_____________________
Write the notation__________________
Answer_______________________
4. Mr. McKelvey surveyed 240 men and 285 women about their vehicles.
Of those surveyed 155 men and 70 women said that they own a red
vehicle. If a person is chosen at random from those surveyed, what is
the probability of choosing a woman or a person that does NOT own a
red vehicle?
Define Event A_____________________
Define Event B_____________________
Write the notation__________________
Answer_________________
5. Tyler spins two spinners that have four equal sections numbered 1
through 4. If he spins a 4 on at least on spin, what is the probability that
the sum of his two spins is an odd number?
Define Event A_____________________
Define Event B_____________________
Write the notation__________________
List sample space:
(1, 1) (2, 1) (3, 1) (4, 1)
(1, 2)
(1, 3)
(1, 4)
Answer_______________________________
6. In Cedartown, the probability that a person plays sports is 65%. The
probability that a person is between the ages of 12 and 18 is 40%. The
probability that a person plays sports and is between the ages of 12 and
18 is 25%. Are the events independent?
Define Event A_____________________
Define Event B_____________________
Write the notation__________________
Answer____________________________
7. A random survey was conducted to gather information about age and
employment status. The table shows the data that were collected.
What is the probability that a randomly selected person surveyed has a
job, given that the person is less than 18 years old?
Define Event A_____________________
Define Event B_____________________
Write the notation__________________
Answer____________________________