A survey of 71 students revealed the following statistics for the mode of transportation used by the students; Taxi (X), bus (B), train (T)
Subject Number of fluent people
X= 50
B= 36
T= 33
X and B= 20
B and T= 18
T and X= 22
X,B and T= 12
How many students take the taxi only?
How many students take the bus only?
How many students take the train only?
------ I NEED TO KNOW HOW TO SOLVE THESE Types of problems...
Subject Number of fluent people
X= 50
B= 36
T= 33
X and B= 20
B and T= 18
T and X= 22
X,B and T= 12
How many students take the taxi only?
How many students take the bus only?
How many students take the train only?
------ I NEED TO KNOW HOW TO SOLVE THESE Types of problems...
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There is a formula, but I would just draw a venn diagram like the one in the link below.
Basically, you first label the 3 circles (one for each mode of transport). Then fill in the weird triangle thing in the middle (the intersection of all 3 circles). In this case it would be 12 because 12 people take all 3 modes of transport.
Next, fill in each of the areas where only 2 of the circles are intersecting (e.g. one of these 3 areas is directly under the "weird triangle thing in the middle" that we filled in first. However, when filling them in you have to remember that you already counted 12 people taking the all 3 modes of transport. So if 22 people take taxi and bus, 12 of these 22 people were already accounted for when you counted the number of people taking all 3 modes of transport. So for the taxi and train intersection you would only put 10 (22 - 12). Same logic for the other intersections: train and bus would have 6, and taxi and bus would have 8.
Finally fill in each of the outer areas (sorta semicircle looking things that do no intersect with anything). Now, for example, if you are filling in the taxi area, you have to take away all the people who take all 3 modes of transport, and all the people who either take taxi and bus or taxi and train (you already counted these people by filling in the other areas). So the number of people who take taxi only would be 50 - 12 - 8 -10 = 20. Same thing for the other 2 outer areas. You would get 36 - 12 - 6 - 8 = 10 people take only the bus, and 33 - 12 - 10 - 6 = 5 people take only the train.
Sorry if its a little confusing.
I can't write the formula (if you find it easier that way) but it is the second equation in the wikipedia link below. If you already did set notation then it will make sense and if you didn't then you can't use it anyways so just stick the venn diagram thing.
Hope this helps.
Basically, you first label the 3 circles (one for each mode of transport). Then fill in the weird triangle thing in the middle (the intersection of all 3 circles). In this case it would be 12 because 12 people take all 3 modes of transport.
Next, fill in each of the areas where only 2 of the circles are intersecting (e.g. one of these 3 areas is directly under the "weird triangle thing in the middle" that we filled in first. However, when filling them in you have to remember that you already counted 12 people taking the all 3 modes of transport. So if 22 people take taxi and bus, 12 of these 22 people were already accounted for when you counted the number of people taking all 3 modes of transport. So for the taxi and train intersection you would only put 10 (22 - 12). Same logic for the other intersections: train and bus would have 6, and taxi and bus would have 8.
Finally fill in each of the outer areas (sorta semicircle looking things that do no intersect with anything). Now, for example, if you are filling in the taxi area, you have to take away all the people who take all 3 modes of transport, and all the people who either take taxi and bus or taxi and train (you already counted these people by filling in the other areas). So the number of people who take taxi only would be 50 - 12 - 8 -10 = 20. Same thing for the other 2 outer areas. You would get 36 - 12 - 6 - 8 = 10 people take only the bus, and 33 - 12 - 10 - 6 = 5 people take only the train.
Sorry if its a little confusing.
I can't write the formula (if you find it easier that way) but it is the second equation in the wikipedia link below. If you already did set notation then it will make sense and if you didn't then you can't use it anyways so just stick the venn diagram thing.
Hope this helps.
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33 take taxi. 12 take taxi and another 2 modes. since it includes those that take taxi plus only one mode, subtract 12 from each that takes taxi plus one. (18-12)+(22-12)=16. 33 -16= 17