Question 1
A)Which of the following formulas is used to mathematically recognize and explain the conditional probability of event A
, given event B
?(1 point)
Responses
P(A and B)=P(A)⋅P(B)
upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis times upper P left parenthesis upper B right parenthesis
P(A|B)=P(A and B)P(A)
upper P left parenthesis upper A vertical bar upper B right parenthesis equals Start Fraction upper P left parenthesis upper A and upper B right parenthesis over upper P left parenthesis upper A right parenthesis End Fraction
P(A|B)=P(A and B)P(B)
upper P left parenthesis upper A vertical bar upper B right parenthesis equals Start Fraction upper P left parenthesis upper A and upper B right parenthesis over upper P left parenthesis upper B right parenthesis End Fraction
P(A and B)=P(A)P(A and B)
upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction upper P left parenthesis upper A right parenthesis over upper P left parenthesis upper A and upper B right parenthesis End Fraction
Question 2
A)Which of the following represents a dependent event?(1 point)
Responses
selecting a number from a set of number cards and putting it back because it was not an even number
selecting a number from a set of number cards and putting it back because it was not an even number
picking 2 snacks from the pantry and replacing the first one before selecting another one
picking 2 snacks from the pantry and replacing the first one before selecting another one
riding your bike, given that it is a sunny day
riding your bike, given that it is a sunny day
picking 2 snacks from the pantry without looking and keeping the first one before selecting the second one
picking 2 snacks from the pantry without looking and keeping the first one before selecting the second one
Question 3
A)There are 100 trading cards in a bin. They include 5 rare cards, 35 limited cards, and the remainder are common cards. Which of the following correctly interprets the probability of choosing 2 rare cards from the bin? Assume that the cards are pulled without replacement.(1 point)
Responses
5100
Start Fraction 5 over 100 End Fraction
5100⋅5100
Start Fraction 5 over 100 End Fraction times Start Fraction 5 over 100 End Fraction
5100+5100
Start Fraction 5 over 100 End Fraction times Start Fraction 5 over 100 End Fraction
5100⋅499
Start Fraction 5 over 100 End Fraction times Start Fraction 4 over 99 End Fraction
Question 4
A)Mr. Jay has 100 pairs of shoes in his closet. He has 26 brown pairs, 12 navy pairs, 47 black pairs, and 15 white pairs. What is P(brown|black)
?(1 point)
Responses
26100⋅47100
Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 100 End Fraction
26100⋅4799
Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 99 End Fraction
26100
Start Fraction 26 over 100 End Fraction
26100+4799
Start Fraction 26 over 100 End Fraction plus Start Fraction 47 over 99 End Fraction
Question 5
A)Bathsheba has 5 paintings in her house, 1 each in a color palette of red, yellow, blue, green, and purple. She hangs them randomly in a horizontal order. What is the probability of hanging the blue painting first, and then the green?(1 point)
Responses
15⋅14
Start Fraction 1 over 5 End Fraction times Start Fraction 1 over 4 End Fraction
15+15
Start Fraction 1 over 5 End Fraction plus Start Fraction 1 over 5 End Fraction
15
A)Which of the following formulas is used to mathematically recognize and explain the conditional probability of event A
, given event B
?(1 point)
Responses
P(A and B)=P(A)⋅P(B)
upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis times upper P left parenthesis upper B right parenthesis
P(A|B)=P(A and B)P(A)
upper P left parenthesis upper A vertical bar upper B right parenthesis equals Start Fraction upper P left parenthesis upper A and upper B right parenthesis over upper P left parenthesis upper A right parenthesis End Fraction
P(A|B)=P(A and B)P(B)
upper P left parenthesis upper A vertical bar upper B right parenthesis equals Start Fraction upper P left parenthesis upper A and upper B right parenthesis over upper P left parenthesis upper B right parenthesis End Fraction
P(A and B)=P(A)P(A and B)
upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction upper P left parenthesis upper A right parenthesis over upper P left parenthesis upper A and upper B right parenthesis End Fraction
Question 2
A)Which of the following represents a dependent event?(1 point)
Responses
selecting a number from a set of number cards and putting it back because it was not an even number
selecting a number from a set of number cards and putting it back because it was not an even number
picking 2 snacks from the pantry and replacing the first one before selecting another one
picking 2 snacks from the pantry and replacing the first one before selecting another one
riding your bike, given that it is a sunny day
riding your bike, given that it is a sunny day
picking 2 snacks from the pantry without looking and keeping the first one before selecting the second one
picking 2 snacks from the pantry without looking and keeping the first one before selecting the second one
Question 3
A)There are 100 trading cards in a bin. They include 5 rare cards, 35 limited cards, and the remainder are common cards. Which of the following correctly interprets the probability of choosing 2 rare cards from the bin? Assume that the cards are pulled without replacement.(1 point)
Responses
5100
Start Fraction 5 over 100 End Fraction
5100⋅5100
Start Fraction 5 over 100 End Fraction times Start Fraction 5 over 100 End Fraction
5100+5100
Start Fraction 5 over 100 End Fraction times Start Fraction 5 over 100 End Fraction
5100⋅499
Start Fraction 5 over 100 End Fraction times Start Fraction 4 over 99 End Fraction
Question 4
A)Mr. Jay has 100 pairs of shoes in his closet. He has 26 brown pairs, 12 navy pairs, 47 black pairs, and 15 white pairs. What is P(brown|black)
?(1 point)
Responses
26100⋅47100
Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 100 End Fraction
26100⋅4799
Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 99 End Fraction
26100
Start Fraction 26 over 100 End Fraction
26100+4799
Start Fraction 26 over 100 End Fraction plus Start Fraction 47 over 99 End Fraction
Question 5
A)Bathsheba has 5 paintings in her house, 1 each in a color palette of red, yellow, blue, green, and purple. She hangs them randomly in a horizontal order. What is the probability of hanging the blue painting first, and then the green?(1 point)
Responses
15⋅14
Start Fraction 1 over 5 End Fraction times Start Fraction 1 over 4 End Fraction
15+15
Start Fraction 1 over 5 End Fraction plus Start Fraction 1 over 5 End Fraction
15
Answers
Answered by
GPT-4o mini
Let's address each question one at a time:
### Question 1
**Which of the following formulas is used to mathematically recognize and explain the conditional probability of event A, given event B?**
**Correct Answer:**
\[ P(A|B) = \frac{P(A \text{ and } B)}{P(B)} \]
This formula correctly represents the conditional probability of event A given event B.
### Question 2
**Which of the following represents a dependent event?**
**Correct Answer:**
**Picking 2 snacks from the pantry without looking and keeping the first one before selecting the second one.**
This event is dependent because the outcome of the first selection affects the outcome of the second selection.
### Question 3
**Which of the following correctly interprets the probability of choosing 2 rare cards from the bin? Assume that the cards are pulled without replacement.**
**Correct Answer:**
\[\frac{5}{100} \cdot \frac{4}{99}\]
This expression captures the probability of first choosing one rare card and then choosing another without replacement.
### Question 4
**What is \( P(brown|black) \)?**
**Correct Answer:**
\[\frac{26}{100} \cdot \frac{47}{99}\]
This interpretation is correct if we consider the conditional probability of choosing brown given that black has already been chosen.
### Question 5
**What is the probability of hanging the blue painting first, and then the green?**
**Correct Answer:**
\[\frac{1}{5} \cdot \frac{1}{4}\]
This probability calculation is correct because there are 5 paintings to choose from initially and then 4 remaining paintings after the first one has been hung.
If you have further questions or need explanations on any of the correct answers, feel free to ask!
### Question 1
**Which of the following formulas is used to mathematically recognize and explain the conditional probability of event A, given event B?**
**Correct Answer:**
\[ P(A|B) = \frac{P(A \text{ and } B)}{P(B)} \]
This formula correctly represents the conditional probability of event A given event B.
### Question 2
**Which of the following represents a dependent event?**
**Correct Answer:**
**Picking 2 snacks from the pantry without looking and keeping the first one before selecting the second one.**
This event is dependent because the outcome of the first selection affects the outcome of the second selection.
### Question 3
**Which of the following correctly interprets the probability of choosing 2 rare cards from the bin? Assume that the cards are pulled without replacement.**
**Correct Answer:**
\[\frac{5}{100} \cdot \frac{4}{99}\]
This expression captures the probability of first choosing one rare card and then choosing another without replacement.
### Question 4
**What is \( P(brown|black) \)?**
**Correct Answer:**
\[\frac{26}{100} \cdot \frac{47}{99}\]
This interpretation is correct if we consider the conditional probability of choosing brown given that black has already been chosen.
### Question 5
**What is the probability of hanging the blue painting first, and then the green?**
**Correct Answer:**
\[\frac{1}{5} \cdot \frac{1}{4}\]
This probability calculation is correct because there are 5 paintings to choose from initially and then 4 remaining paintings after the first one has been hung.
If you have further questions or need explanations on any of the correct answers, feel free to ask!