Question

In a recent semester at a local university, 500 students enrolled in both General Chemistry and Calculus I. Of these students, 66 received an A in general chemistry, 73 received an A in calculus, and 33 received an A in both general chemistry and calculus. Find the probability that a randomly chosen student received an A in general chemistry or calculus or both.

Answer 1

Answer:

$\frac{24}{125}$

Step-by-step explanation:

Given: In a recent semester at a local university, $500$ students enrolled in both General Chemistry and Calculus. Of these students, $66$ received an A in general chemistry, $73$ received an A in calculus, and $33$ 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 $=500$

Total number of students received A in General Chemistry $=66$

Total number of students received A in calculus $=73$

Total number of students received A in General chemistry and calculus both $=33$

Probability that a randomly selected student got A in General Chemistry

$p(\text{GC})=\frac{\text{student got A in Chemistry}}{\text{Total students}}$

$p(\text{GC})=\frac{66}{500}$

Probability that a randomly selected student got A in Calculus

$p(\text{C})=\frac{\text{student got A in Calculus}}{\text{Total students}}$

$p(\text{C})=\frac{73}{500}$

Probability that a randomly selected student got A in General Chemistry and calculus

$p(\text{GC}\cap\text{C})=\frac{\text{student got A in Chemistry and calculus}}{\text{Total students}}$

$p(\text{GC}\cap\text{C})=\frac{33}{500}$

Probability that a randomly chosen student received A in general chemistry or calculus or both

$p(\text{GC}\cup\text{C})=p(\text{C})+p(\text{GC})-p(\text{GC}\cap\text{C})$

$p(\text{GC}\cup\text{C})=\frac{66}{500}+\frac{73}{500}-\frac{33}{500}$

$p(\text{GC}\cup\text{C})=\frac{24}{125}$

Hence the probability that a randomly chosen student received an A in general chemistry or calculus or both is $\frac{24}{125}$