Mike R. answered • 11/13/16
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Math Teacher, Regents, AP, SAT, ACT
No need to overthink this problem. If 120 students took math and there were 200 total students, the probability that a student was taken from the group took math would be 120/200, which reduces to 3/5
Mike R.
Draw a Venn Diagram: two circles with a box around them. Label one circle math and the other one history. 20 take both math and history, so put the number 20 in the middle. The problem says that 120 students took math, so that means that the section of the math circle who took MATH ONLY would equal 100. That way, the total in the math circle equals 120. Likewise, because 70 students took history, the section of the history circle who took HISTORY ONLY would equal 50. When you add the number of students who took MATH OR HISTORY, that would equal 170, so that means 30 students took neither math nor history. That number is placed inside the box but not within any circle.
When you add the two sections of the math circle (100+20), that equals 120.
The probability that a student chosen at random from the group took math would equal 120/200, or 3/5
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11/13/16
Elizabeth H.
11/13/16