Name:_________________________________________per.____
PSU Stats – Section 4-3 NOTES & Warm-up
WARM-up:
DETERMINE if each event is Independent or Dependent; then calculate the probability of Event A AND B occurring.
Leave answer in fractional form.
1 . A: When a month is randomly selected and ripped from a calendar and destroyed, it is July.
B: When a different month is randomly selected and ripped from a calendar and destroyed, it is November.
Independent
or
Dependent
P(A and B) =
2. A: When the first digit (0 thru 9) of a four-digit lottery number is chosen by someone buying a ticket, it is the same
first digit that is later drawn in the official lottery.
B: When the second digit (0 thru 9) of a four-digit lottery number is chosen by someone buying a ticket, it is the same
second digit that is later drawn in the official lottery.
Independent
or
Dependent
P(A and B) =
3. You turn to create two situations and calculate the probability:
A:
B:
Independent
or
Conditional Probability Rule:
𝑃(𝐵|𝐴) =
𝑃(𝐴 𝑎𝑛𝑑 𝐵)
𝑃(𝐴)
Dependent
P(A and B) =
Denominator Check!_________________________
A=
B=
Example: The probability that Sam parks in a no-parking zone and gets a parking ticket is 0.06,
and the probability that Sam cannot find a legal parking space and has to park in the no parking
zone is 0.20. On Tuesday, Sam arrives at school and has to park in a no-parking zone.
Find the probability that he will get a parking ticket.
𝑃 (𝐵|𝐴) =
Table of Conditional Probabilities:
ATLEAST Probabilities:
Example 1: Computer Ownership At a local university 54.3% of
incoming first-year students have computers. If 3 students
are selected at random, find the following probabilities.
a. None have computers.
b. At least one has a computer.
c. All have computers
Example 2: High School Grades of First-Year College Students
Forty-seven percent of first-year college students
enrolled in 2005 had an average grade of A in high
school compared to 20% of first-year college students
in 1970. Choose 6 first-year college students at random
enrolled in 2005. Find the probability that
a. All had an A average in high school
b. None had an A average in high school
c. At least 1 had an A average in high school
Tree Diagrams:
Example 1: Sales A manufacturer makes two models of an item: model I, which accounts for 80% of unit sales, and
model II, which accounts for 20% of unit sales. Because of defects, the manufacturer has to replace (or exchange) 10% of
its model I and 18% of its model II. If a model is selected at random, find the probability that it will be defective.
Example 2: