# SOLUTION: a survey of a school 0f 850 students found that 150 used a bus to get to school, 75 used a train and 650 user neither. using a venn diagram, calculate the number of students who us

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 Click here to see ALL problems on Probability-and-statistics Question 148876: a survey of a school 0f 850 students found that 150 used a bus to get to school, 75 used a train and 650 user neither. using a venn diagram, calculate the number of students who used both a bus and a train to get to school.Answer by Edwin McCravy(8880)   (Show Source): You can put this solution on YOUR website!a survey of a school 0f 850 students found that 150 used a bus to get to school, 75 used a train and 650 user neither. using a venn diagram, calculate the number of students who used both a bus and a train to get to school. ``` Imagine you have all 850 students in the bleachers of football field. First draw a big rectangle to represent, say, a big football field, for all 850 students to come down and stand in. Now on that football field draw a big circle for all 150 students to stand in who used a bus and label it B: Next draw another big circle overlapping it for all 75 students to stand in who used a train and label it T: Now the 650 students who use neither bus nor train will have to stand on the field outside both circles, so we'll write 650 out there to stand for the 650 students who will stand out there: We need to know how many people will be standing in both circles, that is, how many will be standing in this overapping part of the two circles: ` So we'll let represent the number of students in that region, so we'll write "x" in there: ` and in the main drawing: Since there are 150 students who used a bus, the rest of those 150 besides the x that used both, that is, 150-x, will have to stand in this region, in which we write 150-x: and in the main drawing: --- Since there are 75 students who used a train, the rest of those 75 besides the x that used both, that is, 75-x, will have to stand in this region, in which we write 75-x: ` ` and in the main drawing: Now we add up all the numbers in the four regions and that sum must equal the entire 850 students standing somewhere on the football field: Solve that and get The answer is 25 students used both bus and train. ---- If you didn't have to use a Venn diagram, you could have done it easier with this formula: N(B or T) = N(B) + N(T) - N(B and T) 850-650 = 150 + 75 - N(B and T) 200 = 225 - N(B and T) N(B and T) = 225 - 200 N(N and T) = 25. Edwin```