A survey of 100 randomly selected students gave the following information. 45 students are taking mathematics. 41
Question:
A survey of 100 randomly selected students gave the following information.
45 students are taking mathematics.
41 students are taking English.
40 students are taking history.
15 students are taking math and English.
18 students are taking math and history.
17 students are taking English and history.
7 students are taking all three.
a. How many are taking only mathematics?
b. How many are taking only English?
c. How many are taking only history?
d. How many are not taking any of these courses?
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Step by Step Answer:
We use Plyas problemsolving guidelines for this example Step 4 Add all the numbers listed in the sets of the Venn diagram to see that 83 students have been accounted for Since 100 students were surveyed we see that 17 are not taking any of the three courses We also filled in this number in Figure 216c We now have the answers to the questions directly from the Venn diagram a 19 b 16 c 12 d 17 Look Back Does our answer make sense Add all the numbers in the Venn diagram as a check to see that we have accounted for the 100 students Understand the Problem We are considering students who are members of one or more of three sets If U represents the universe then U 100 We also define the three sets M students taking mathematics E students taking English and H students taking history Devise a Plan The plan is to draw a Venn diagram and then to fill in the various regions We fill in the innermost region first and then work our way outward using subtraction until the numbers of elements of the eight regions formed by the three sets are known Carry Out the Plan Step 1 We note MEH 7 in Figure 216a Step 2 Fill in the other inner portions EH 17 but 7 have previously been accounted for so an additional 10 members 17 7 10 are added to the Venn diagram see Figure 216b MH 18 fill in 18 7 11 ME 15 fill in 15 7 8 Step 3 Fill in the other regions see Figure 216c H 40 but 28 have previously been accounted for in the set ...View the full answer
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GERALD KAMAU
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