Question 10·Easy·Probability and Conditional Probability
The table below shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools.
| High school | 2008 | 2009 | 2010 | 2011 | 2012 |
|---|---|---|---|---|---|
| Foothill | 87 | 80 | 75 | 76 | 70 |
| Valley | 44 | 54 | 65 | 76 | 82 |
| Total | 131 | 134 | 140 | 152 | 152 |
Of the students who completed a summer internship in 2010, which of the following represents the fraction of students who were from Valley High School?
For table-based fraction or probability questions, first isolate the correct row/column that matches the condition in the question (here, the year 2010). Next, decide clearly what the numerator and denominator should be: the numerator is the specific group the question asks about (Valley students), and the denominator is the relevant total for that situation (all students that year). Form the fraction as part/whole, then match it directly to the answer choices without doing extra calculations you do not need.
Hints
Narrow to the correct year
Ignore all years except 2010. Only use the numbers in the 2010 column of the table.
Decide what goes on top and bottom of the fraction
The question asks for the fraction of 2010 interns who were from Valley. Which number should be the part (numerator), and which should be the whole (denominator)?
Use the table values correctly
Use the number of Valley students in 2010 as the numerator and the total number of students in 2010 (bottom row) as the denominator. Then look for that fraction in the answer choices.
Desmos Guide
Compute the fraction for Valley in 2010
From the table, identify Valley's number in 2010 and the total number of students in 2010. In Desmos, type the fraction with Valley's 2010 count as the numerator and the 2010 total as the denominator (for example, something like Valley_number_2010/Total_2010) to see its decimal value or simplified fraction.
Compare with the answer choices
Type each answer choice into its own line in Desmos (for example, 10/140, 75/140, etc.) and compare their values to the value of the fraction you found. The correct answer choice is the one whose value matches exactly the fraction for Valley in 2010.
Step-by-step Explanation
Focus on the correct year and question
The question asks about 2010 only and wants the fraction of students who were from Valley High School out of all students who completed an internship in 2010.
So we are looking for:
- Numerator: number of Valley students in 2010.
- Denominator: total number of students in 2010.
Read the needed values from the table
From the 2010 column in the table:
- Valley High School has 65 students.
- The total number of students (bottom row) is 140.
These are the only two numbers we need to form the fraction.
Form the fraction and match it to an answer choice
The fraction of 2010 interns who were from Valley is:
- Numerator = Valley students in 2010 = 65.
- Denominator = total students in 2010 = 140.
So the fraction is , which corresponds to choice B.