1. Concept Recap 12.1-12.2 Sample Space: product of 2 number cubes
Frequency Table
Probability Distribution Graph
Product
# ocurrences
Even
Odd 1 2 3 4 5 6 8 10 12 9 15 18 16 20 24 25 30 36

2. KEY CONCEPTS AND VOCABULARY
When events A and B are dependent, the probability of B occurring depends on whether
A has already occurred. This kind of probability is called conditional probability.
The probability of B given that A has occurred is written as V

3. CHARACTERISTICS OF STUDENT VOLUNTEERS
EXAMPLE 1: FINDING CONDITIONAL PROBABILITY
Use the table to find each probability. a) P(volunteer a junior) 39/80 b) P(volunteer female) 37/80 c) P(volunteer a senior and male) 25/80 d) P(volunteer a junior | volunteer female) 21/37 e) P(volunteer male | volunteer a senior) 25/41
CHARACTERISTICS OF STUDENT VOLUNTEERS
GRADE LEVEL
MALE
FEMALE
JUNIOR 18 21
SENIOR 25 16

4. EXAMPLE 2: FINDING CONDITIONAL PROBABILITY
Students were surveyed regarding their favorite out of blue, green, red, and orange. Their gender was also recorded.
Find the probability that a student is a boy, given that the student prefers red.
62%; 62% of the students who prefer red are males
Find the probability that a student prefers blue, given that the student is a girl.
42.5%; 42.5% of the students who are female like blue
Find the probability that a student is a girl, given that the student prefers green.
47%; 47% of the students who like green are girls
FAVORITE COLOR
GENDER
BLUE
RED
GREEN
ORANGE
TOTAL
MALE 12 16 9 3 40
FEMALE 17 10 8 5 29 26 80

5. EXAMPLE 3: CREATING A TREE DIAGRAM
Suppose a class is 55% male. Of the males, 34% are at least 68 inches tall. Of the females, 12% are at least 68 inches tall. a) Create a tree diagram.
34%
At Least 68in
Male
55%
Under 68in
66%
12%
At Least 68in
45%
Under 68in
Female
88%

6. EXAMPLE 3: Interpreting A TREE DIAGRAM
P(Under 68 inches and Male)
.55∗.66= 36.3%
P(At Least 68 inches and Male)
.55∗.34=18.7%
d) P(Under 68 inches and Female)
.45∗.88=39.6%
e) P(At Least 68 inches and Female)
  .45∗.12= 5.4%
P(at least 68in|female) = 12%
g) P(under 68in|male) = 66%
H) P(under 68 in)
.55 ∗ ∗.88= 75.9%
34%
At Least 68in
Male
55%
Under 68in
66%
12%
At Least 68in
45%
Under 68in
Female
88%