Question

10. A school is trying to schedule periods of Chemistry and Algebra II.

Answer 1

Answer:

~62%

Step-by-step explanation:

Let n(A) be the number of students signed up for Algebra II.

Given that n(A) = 298

Let n(B) be the number of students signed up for Chemistry.

Given that n(B) = 328

n(A $\cup$ B) will be the number of students who have signed up for either one or both of two subjects.

n(A $\cup$ B) = 386

Formula for n(A $\cup$ B):

n(A $\cup$ B) = n(A) + n(B) - n(A $\cap$ B)

Where n(A $\cap$ B) is the number of students signed up for both the courses.

Putting the values in the formula above:

386 = 298 + 328 - n(A $\cap$ B)

n(A $\cap$ B) = 240

Formula for Probability of an event E:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(A \cap B) = \dfrac{n(A \cup B) }{n(A \cap B)}$

$\Rightarrow P(A \cap B) = \dfrac{240 }{386}\\\Rightarrow P(A \cap B) = 62.17\%$

Hence, the required probability is ~62%