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:

Question

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)

Answer 1

**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.