(06.05 mc) a group of students were surveyed to find out if they like bike riding and/or roller skating as a hobby. the results of the survey are shown below: 80 students like bike riding 20 students like bike riding but do not like skating 90 students like skating 40 students do not like bike riding 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 bike riding and skating? show your work. (5 points) part b: what is the probability that a student who does not like bike riding also does not like skating? explain your answer. (5 points)

I made a two-way table by overlapping two like-dislike data tables.  At the end of each row and column, I included a total.  I filled in the information given [see the first picture].

Next, I was able to fill in missing values [see the second picture].  For the likes-biking column, there were 80 total and 20 who didn't like ice skating.  Therefore, there must have been 60 who did like ice skating (80 - 20 = 60).  Next, I did the same thing with the likes-skating column: 90 - 60 = 30.  Then, I could fill in the last intersection point, the students who didn't like either skating or biking: 40 - 30 = 10.

To complete the table, I added in the totals at the end of the rows and columns, as well as the total number of students surveyed, represented in the bottom right box. [see the third picture].

Part A:  There were 60 students who liked both activities, and 120 students total.  The percentage is calcuated like this: 

Part B:  For this probability, take the number of students that don't like biking or skating out of the total number of biking: 

Agc and bgd are vertical angles