Agroup 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.

part b: what is the probability that a student who does not like watching television also does not like reading? explain your answer.

A. 53.8% of students like both reading and TV. Reason: If 90 people like TV and 20 of those people do not like reading, the other 70 must like reading. Since 40 people don't like TV we must have a total of 130 people (90+40). This means that of those 130 people 53.8% like both.

B. 23.1% of students do not like reading or TV. Reason: There are 130 total answers. We know that 70 of those people like both TV and reading (see answer A). Another 20 of those people like TV, but not reading. This leaves 40 people who either like reading but not tv or like neither. Looking at the chart, you can see that 40 people dislike TV, so this make sense. You can also see that 50 people dislike reading. This includes both the people who like TV and dislike reading and the people who dislike TV and reading. Taking out the 20 people who like TV, 30 people dislike both, meaning that the remaining 10 people like reading but not TV. If 30 out of 130 people like neither, the percentage is 23.1%.