A group of students were surveyed to find out if they like watching television or reading during their free time. The results of the survey are shown below:
90 students like watching television
20 students like watching television but do not like reading
80 students like reading
40 students do not like watching television
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 watching television and reading? Show your work. (5 points)
Part B: What is the probability that a student who does not like watching television also does not like reading? Explain your answer. (5 points)
To create a two-way table, we can divide the students into four categories: like watching television and reading, like watching television but not reading, like reading but not watching television, and not like watching television.
| | Like Reading | Not Like Reading | Total |
|--------------------|--------------|------------------|-------|
| Like TV | ? | 20| 90 |
| Not Like TV | 60 | 40| 100|
| Total | 80 | 60| 190|
Part A:
To find out the number of students who like both watching television and reading, we need to subtract the students who like watching television but do not like reading (20) from the total number of students who like watching television (90):
? = 90 - 20 = 70
The percentage of students who like both watching television and reading is:
(70 / 190) * 100% ≈ 36.8%
Part B:
The probability that a student who does not like watching television also does not like reading can be found by dividing the number of students who do not like both activities (40) by the total number of students who do not like watching television (100):
P(not like reading | not like TV) = 40 / 100 = 0.4
The probability that a student who does not like watching television also does not like reading is 0.4 or 40%. This means 40% of the students who do not like watching television also do not like reading.