Answer:
[tex]\frac{24}{125}[/tex]
Step-by-step explanation:
Given: In a recent semester at a local university, [tex]500[/tex] students enrolled in both General Chemistry and Calculus. Of these students, [tex]66[/tex] received an A in general chemistry, [tex]73[/tex] received an A in calculus, and [tex]33[/tex] received an A in both general chemistry and calculus.
To Find: Find the probability that a randomly chosen student received an A in general chemistry or calculus or both.
Solution:
Total number of students in university [tex]=500[/tex]
Total number of students received A in General Chemistry [tex]=66[/tex]
Total number of students received A in calculus [tex]=73[/tex]
Total number of students received A in General chemistry and calculus both [tex]=33[/tex]
Probability that a randomly selected student got A in General Chemistry
[tex]p(\text{GC})=\frac{\text{student got A in Chemistry}}{\text{Total students}}[/tex]
[tex]p(\text{GC})=\frac{66}{500}[/tex]
Probability that a randomly selected student got A in Calculus
[tex]p(\text{C})=\frac{\text{student got A in Calculus}}{\text{Total students}}[/tex]
[tex]p(\text{C})=\frac{73}{500}[/tex]
Probability that a randomly selected student got A in General Chemistry and calculus
[tex]p(\text{GC}\cap\text{C})=\frac{\text{student got A in Chemistry and calculus}}{\text{Total students}}[/tex]
[tex]p(\text{GC}\cap\text{C})=\frac{33}{500}[/tex]
Probability that a randomly chosen student received A in general chemistry or calculus or both
[tex]p(\text{GC}\cup\text{C})=p(\text{C})+p(\text{GC})-p(\text{GC}\cap\text{C})[/tex]
[tex]p(\text{GC}\cup\text{C})=\frac{66}{500}+\frac{73}{500}-\frac{33}{500}[/tex]
[tex]p(\text{GC}\cup\text{C})=\frac{24}{125}[/tex]
Hence the probability that a randomly chosen student received an A in general chemistry or calculus or both is [tex]\frac{24}{125}[/tex]
