Question

2. Based on the current data, what is ths probability a new student enrolled in a science course is also enrolled in a math couse: Give your answer as a fraction in lowest terms.
3. Based on the current data, what is the probability a new student enrolled in a science course is also enrolled in a math and humanities course? Give your answer as a fraction in lowest terms.

Answer 1

Answer:

see the works below.

Step-by-step explanation:

Probability of an Event = the fraction of an event out of the total:

$\boxed{Probability\ (P(X))=\frac{possibilities\ of\ event\ (n(X))}{total\ possibilities\ (n(S))} }$

Let:

A = student enrolls into a humanities course

B = student enrolls into a science course

C = student enrolls in a science and math courses

D = student enrolls in a science + math + humanities courses

Given:

Total students (n(S)) = 578

n(A) = 47 + 22 + 22 + 9 + 18 + 37 + 15 = 170 (total of students inside Circle Humanities)

n(B) = 76 + 22 + 22 + 9 + 18 + 40 + 27 = 214 (total of students inside Circle Science)

n(C) = 9 + 18 + 27 + 40 = 94 (overlapping of  Circle Science & Circle Math)

n(D) = 9 + 18 = 27 (overlapping of  Circle Science & Circle Math & Circle Humanities)

Probability of a student enrolls in Humanities (P(A)):

$\displaystyle P(A)=\frac{n(A)}{n(S)}$

        $\displaystyle =\frac{170}{578}$

        $\displaystyle =\frac{5}{17}$

Probability of a student enrolls in Science (P(B)):

$\displaystyle P(B)=\frac{n(B)}{n(S)}$

        $\displaystyle =\frac{214}{578}$

        $\displaystyle =\frac{107}{289}$

Probability of a student enrolls in Science & Math (P(C)):

$\displaystyle P(C)=\frac{n(C)}{n(S)}$

        $\displaystyle =\frac{94}{578}$

        $\displaystyle =\frac{47}{289}$

Probability of a student enrolls in Science & Math & Humanities (P(D)):

$\displaystyle P(D)=\frac{n(D)}{n(S)}$

        $\displaystyle =\frac{27}{578}$