Question

three hundred high school seniors were surveyed about their intended college majors. the results are displayed in the venn diagram below: if a student is randomly selected from the group, what is the probability that they are majoring in both math and science? round your answer to the nearest whole percent. 10% 17% 33%

Explanation:

Step1: Find total number of students

The total number of students surveyed is 300.

Step2: Set up an equation for the Venn - Diagram

Let the number of students majoring in both math and science be $x$. Then $120 + x+50 + 100=300$.

Step3: Solve for $x$

Simplify the left - hand side of the equation: $270 + x=300$. Subtract 270 from both sides: $x = 300 - 270=30$.

Step4: Calculate the probability

The probability $P$ that a randomly selected student is majoring in both math and science is $P=\frac{30}{300}=0.1$.

Step5: Convert to percentage

$0.1\times100\% = 10\%$.

Answer:

10%