Find the sample space for the gender of the children if a family has three children. Use B for boy and G for girl. Include order. For example, BBG and.
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Find the sample space for the gender of the children if a family has three children. Use B for boy and G for girl. Include order. For example, BBG and BGB are different outcomes.
Bell Ringer
Solution (Using a Tree Diagram)
B
B
B
BB
B
B
G
G
G G
G
G
G
BBG
S = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}
CHAPTER 15 PART 1
Probability Rules
Addition Rule
๐ท ( ๐จโช๐ฉ)=๐ท ( ๐จ )+๐ท (๐ฉ )โ๐ท (๐จโฉ๐ฉ)
Note: If A and B are disjoint, we just use P(A) + P(B)
A survey of college students found that 56% live in a campus residence hall, 62% participate in a campus meal program, and 42% do both. Let A = student living on campus and B = student has a meal plan
Are living on campus and having a meal plan independent? Are they disjoint?They are independent, but they are not disjoint.
A survey of college students found that 56% live in a campus residence hall, 62% participate in a campus meal program, and 42% do both. Whatโs the probability that a randomly selected student either lives or eats on campus?
๐ ( ๐ดโช๐ต )=๐ ( ๐ด )+๐ (๐ต )โ ๐ (๐ดโฉ๐ต)
๐ ( ๐ดโช๐ต )=.56+.62โ .42=0.76
Let A = student living on campus and B = student has a meal plan
A survey of college students found that 56% live in a campus residence hall, 62% participate in a campus meal program, and 42% do both.
0.42 0.200.14
A B
0.24
Venn Diagra
m
Conditional Probability๐ท (๐ฉโจ๐จ)= ๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐ ๐๐ ๐ฉ ๐๐๐๐๐ ๐จ
๐ท (๐ฉโจ๐จ)=๐ท (๐จโฉ๐ฉ)๐ท (๐จ)
From before, 56% of students live on campus, 62% have meal plans, 42% do both. What is the probability that someone with a meal plan is also living on campus?๐ (๐๐๐๐๐๐๐ข๐ |๐๐๐๐๐๐๐๐ )= ๐ (๐๐๐๐๐๐๐๐โฉ๐๐๐๐๐๐๐ข๐ )
๐ (๐๐๐๐๐๐๐๐)
๐ (๐๐๐๐๐๐๐ข๐ |๐๐๐๐๐๐๐๐ )=0.420.62
=0.677
Conditional Probability and Independent Events
then events A and B are independent
According to a pet owners survey, 39% of U.S. households own at least one dog and 34% of U.S. households own at least one cat. Assume that 60% of U.S. households own a cat or a dog.
1. What is the probability that a randomly selected U.S. household owns neither a cat nor a dog?
2. What is the probability that a randomly selected U.S. household owns both a cat and a dog?
3. What is the probability that a randomly selected U.S. household owns a cat if the household owns a dog?
According to a pet owners survey, 39% of U.S. households own at least one dog and 34% of U.S. households own at least one cat. Assume that 60% of U.S. households own a cat or a dog.
1. What is the probability that a randomly selected U.S. household owns neither a cat nor a dog?
ยฟ1โ0.60=0.40
According to a pet owners survey, 39% of U.S. households own at least one dog and 34% of U.S. households own at least one cat. Assume that 60% of U.S. households own a cat or a dog.
2. What is the probability that a randomly selected U.S. household owns both a cat and a dog?P (catโช๐๐๐ )=๐ (๐๐๐ก )+๐ (๐๐๐ )โ๐ (๐๐๐กโฉ๐๐๐)
0.60 = 0.34 + 0.39 โ x x=0.13
0.34 0.39 unknown
0.60
๐ (๐๐๐กโฉ๐๐๐ )=0.13
According to a pet owners survey, 39% of U.S. households own at least one dog and 34% of U.S. households own at least one cat. Assume that 60% of U.S. households own a cat or a dog.
3. What is the probability that a randomly selected U.S. household owns a cat if the household owns a dog?
๐ (๐๐๐ก|๐๐๐ )= ๐ (๐๐๐กโฉ๐๐๐)๐ (๐๐๐)
=0.130.39
=0.33
Todayโs AssignmentRead Chapter 15 Add to HW #9: page 361 #1-4
Chapter 14,15,16 will be included in HW #9 โ Due after Thanksgiving Break
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