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To solve this you must use a proportion like so...
The total number of students that can be chosen are 4,663. This number will represent the whole of one fraction in the proportion. We want to know what percent probability out of these students are engineer, medical doctor/surgeon. This would be considered the part of this fraction. Sum the number of engineering students (615) with medical doctors/surgeons (723) to find this number
723 + 615 = 1,338 students that want to be an engineer or medical doctor/surgeon
Percent's are always taken out of the 100. This means that the other fraction in the proportion will have 100 as the whole and x (the unknown) as the part.
Here is your proportion:
Now you must cross multiply
1,338*100 = 4,663*x
133,800 = 4,663x
To isolate x divide 4,663 to both sides
133,800/4,663 = 4,663x/4,663
28.7 = x
This means that there is a 28.7% of a student with the intent of becoming an engineer or a medical doctor/surgeon to be chosen at random
Hope this helped!
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