Question
Galina spins a spinner with three equally sized colored sections: red, green, and purple. She also rolls a number cube. Which event below has the highest likelihood of occurring?(1 point)
Responses
The spinner lands on red, and the number cube lands on an even number.
The spinner lands on red, and the number cube lands on an even number.
The spinner lands on either purple or red, and the number cube lands on 3.
The spinner lands on either purple or red, and the number cube lands on 3.
The spinner lands on red, and the number cube lands on 6.
The spinner lands on red, and the number cube lands on 6.
The spinner lands on either green or red, and the number cube lands on 6.
Responses
The spinner lands on red, and the number cube lands on an even number.
The spinner lands on red, and the number cube lands on an even number.
The spinner lands on either purple or red, and the number cube lands on 3.
The spinner lands on either purple or red, and the number cube lands on 3.
The spinner lands on red, and the number cube lands on 6.
The spinner lands on red, and the number cube lands on 6.
The spinner lands on either green or red, and the number cube lands on 6.
Answers
GPT-4o mini
To determine which event has the highest likelihood of occurring, we need to calculate the probability of each event.
1. **The spinner lands on red, and the number cube lands on an even number.**
- Probability of landing on red = 1/3 (since there are 3 sections)
- Probability of landing on an even number (2 or 4 or 6) = 3/6 = 1/2
- Combined probability = (1/3) * (1/2) = 1/6
2. **The spinner lands on either purple or red, and the number cube lands on 3.**
- Probability of landing on purple or red = 2/3
- Probability of landing on 3 = 1/6
- Combined probability = (2/3) * (1/6) = 2/18 = 1/9
3. **The spinner lands on red, and the number cube lands on 6.**
- Probability of landing on red = 1/3
- Probability of landing on 6 = 1/6
- Combined probability = (1/3) * (1/6) = 1/18
4. **The spinner lands on either green or red, and the number cube lands on 6.**
- Probability of landing on green or red = 2/3
- Probability of landing on 6 = 1/6
- Combined probability = (2/3) * (1/6) = 2/18 = 1/9
Now let's compare the probabilities:
- Event 1: 1/6
- Event 2: 1/9
- Event 3: 1/18
- Event 4: 1/9
The highest probability is for the **first event**: "The spinner lands on red, and the number cube lands on an even number," which has a probability of 1/6.
1. **The spinner lands on red, and the number cube lands on an even number.**
- Probability of landing on red = 1/3 (since there are 3 sections)
- Probability of landing on an even number (2 or 4 or 6) = 3/6 = 1/2
- Combined probability = (1/3) * (1/2) = 1/6
2. **The spinner lands on either purple or red, and the number cube lands on 3.**
- Probability of landing on purple or red = 2/3
- Probability of landing on 3 = 1/6
- Combined probability = (2/3) * (1/6) = 2/18 = 1/9
3. **The spinner lands on red, and the number cube lands on 6.**
- Probability of landing on red = 1/3
- Probability of landing on 6 = 1/6
- Combined probability = (1/3) * (1/6) = 1/18
4. **The spinner lands on either green or red, and the number cube lands on 6.**
- Probability of landing on green or red = 2/3
- Probability of landing on 6 = 1/6
- Combined probability = (2/3) * (1/6) = 2/18 = 1/9
Now let's compare the probabilities:
- Event 1: 1/6
- Event 2: 1/9
- Event 3: 1/18
- Event 4: 1/9
The highest probability is for the **first event**: "The spinner lands on red, and the number cube lands on an even number," which has a probability of 1/6.