Question
A group of students were surveyed to find out if they like building snowmen or skiing as a winter activity. The results of the survey are shown below:
60 students like building snowmen
10 students like building snowmen but do not like skiing
80 students like skiing
50 students do not like building snowmen
Make a two-way table to represent the data and use the table to answer the following questions.
Part A: What percentage of the total students surveyed like both building snowmen and skiing? Show your work. (5 points)
Part B: What is the probability that a student who does not like building snowmen also does not like skiing? Explain your answer. (5 points)
60 students like building snowmen
10 students like building snowmen but do not like skiing
80 students like skiing
50 students do not like building snowmen
Make a two-way table to represent the data and use the table to answer the following questions.
Part A: What percentage of the total students surveyed like both building snowmen and skiing? Show your work. (5 points)
Part B: What is the probability that a student who does not like building snowmen also does not like skiing? Explain your answer. (5 points)
Answers
GPT 3.5
**Two-way table:**
| | Building Snowmen | Not Building Snowmen | Total |
|-----------------|------------------|----------------------|-------|
| Skiing | 0 | 80 | 80 |
| Not Skiing | 10 | 50 | 60 |
| Total | 60 | 130 | 140 |
**Part A:**
Percentage of students who like both building snowmen and skiing:
= (Number of students who like both activities / Total number of students surveyed) * 100
= (0 / 140) * 100
= 0%
Therefore, 0% of the total students surveyed like both building snowmen and skiing.
**Part B:**
The probability that a student who does not like building snowmen also does not like skiing can be calculated as follows:
= (Number of students who do not like building snowmen and do not like skiing) / Total number of students who do not like building snowmen)
= 50 / (10 + 50)
= 50 / 60
= 5 / 6
Therefore, the probability that a student who does not like building snowmen also does not like skiing is 5/6 or approximately 83.33%. This means that 83.33% of the students who do not like building snowmen also do not like skiing.
| | Building Snowmen | Not Building Snowmen | Total |
|-----------------|------------------|----------------------|-------|
| Skiing | 0 | 80 | 80 |
| Not Skiing | 10 | 50 | 60 |
| Total | 60 | 130 | 140 |
**Part A:**
Percentage of students who like both building snowmen and skiing:
= (Number of students who like both activities / Total number of students surveyed) * 100
= (0 / 140) * 100
= 0%
Therefore, 0% of the total students surveyed like both building snowmen and skiing.
**Part B:**
The probability that a student who does not like building snowmen also does not like skiing can be calculated as follows:
= (Number of students who do not like building snowmen and do not like skiing) / Total number of students who do not like building snowmen)
= 50 / (10 + 50)
= 50 / 60
= 5 / 6
Therefore, the probability that a student who does not like building snowmen also does not like skiing is 5/6 or approximately 83.33%. This means that 83.33% of the students who do not like building snowmen also do not like skiing.