Question
Uniform and Non-Uniform Probability
A regular deck of playing cards has 26 red cards and 26 black cards. There are 12 face cards in a deck.
Question 1
Which is an example of non-uniform probability?
Responses
A drawing a red card from the deckdrawing a red card from the deck
B drawing a black card from the deckdrawing a black card from the deck
C drawing a face card from the deckdrawing a face card from the deck
D not drawing a red card from the decknot drawing a red card from the deck
Question 2
Which statement BEST describes a uniform probability model?
Responses
A All outcomes are equally likely to occur.All outcomes are equally likely to occur.
B One outcome has a greater chance of occurring.One outcome has a greater chance of occurring.
C The desired outcome is certain to occur.The desired outcome is certain to occur.
D No desired outcome is possible.
A regular deck of playing cards has 26 red cards and 26 black cards. There are 12 face cards in a deck.
Question 1
Which is an example of non-uniform probability?
Responses
A drawing a red card from the deckdrawing a red card from the deck
B drawing a black card from the deckdrawing a black card from the deck
C drawing a face card from the deckdrawing a face card from the deck
D not drawing a red card from the decknot drawing a red card from the deck
Question 2
Which statement BEST describes a uniform probability model?
Responses
A All outcomes are equally likely to occur.All outcomes are equally likely to occur.
B One outcome has a greater chance of occurring.One outcome has a greater chance of occurring.
C The desired outcome is certain to occur.The desired outcome is certain to occur.
D No desired outcome is possible.
Answers
GPT-4o mini
### Question 1
The question asks for an example of non-uniform probability. Non-uniform probability occurs when not all outcomes are equally likely. In a standard deck:
- **A** (drawing a red card) has a probability of \( \frac{26}{52} = \frac{1}{2} \)
- **B** (drawing a black card) also has a probability of \( \frac{26}{52} = \frac{1}{2} \)
- **C** (drawing a face card) specifically refers to the 12 face cards (3 face cards of each suit), which gives a probability of \( \frac{12}{52} \), which is not equal to \( \frac{1}{2} \).
- **D** (not drawing a red card) has a probability of \( \frac{26}{52} = \frac{1}{2} \)
**Correct Answer: C (drawing a face card from the deck)**, as this outcome does not have an equal probability to the others.
### Question 2
The question asks for the statement that best describes a uniform probability model, which is characterized by all outcomes having equal probability of occurrence.
- **A** states that all outcomes are equally likely to occur, which defines a uniform probability model.
- **B** indicates that one outcome has a greater chance, which is contrary to uniform probability.
- **C** suggests that the desired outcome is certain, which describes certainty rather than uniformity.
- **D** indicates that no desired outcome is possible, which does not relate to uniformity.
**Correct Answer: A (All outcomes are equally likely to occur.)**
The question asks for an example of non-uniform probability. Non-uniform probability occurs when not all outcomes are equally likely. In a standard deck:
- **A** (drawing a red card) has a probability of \( \frac{26}{52} = \frac{1}{2} \)
- **B** (drawing a black card) also has a probability of \( \frac{26}{52} = \frac{1}{2} \)
- **C** (drawing a face card) specifically refers to the 12 face cards (3 face cards of each suit), which gives a probability of \( \frac{12}{52} \), which is not equal to \( \frac{1}{2} \).
- **D** (not drawing a red card) has a probability of \( \frac{26}{52} = \frac{1}{2} \)
**Correct Answer: C (drawing a face card from the deck)**, as this outcome does not have an equal probability to the others.
### Question 2
The question asks for the statement that best describes a uniform probability model, which is characterized by all outcomes having equal probability of occurrence.
- **A** states that all outcomes are equally likely to occur, which defines a uniform probability model.
- **B** indicates that one outcome has a greater chance, which is contrary to uniform probability.
- **C** suggests that the desired outcome is certain, which describes certainty rather than uniformity.
- **D** indicates that no desired outcome is possible, which does not relate to uniformity.
**Correct Answer: A (All outcomes are equally likely to occur.)**