Question

A class of 160 students contains 40 honor students, 60 athletes, and 80 who are neither athletes nor honor students. From the entire group a student is chosen at random. The fraction equation that proves the events "honor student" and "athlete" are not independent is ____.

Answer 1

1 / 8 is not equal to 3 / 32

Answer 2

Answer with explanation:

Number of Students in the Class =160

Out of which,

Number of honor Students = 40

Number of Athletes = 60

Number of Students who are neither athletes nor honor students=80

⇒   Total Number of students in the class - n (A ∪ B)= 80

⇒160 -80=n(A∪B)

⇒n (A ∪ B)=80

⇒n (A ∪ B)=n(A) + n(B) - n(A ∩ B)

⇒80= 40 +60 - n(A ∩ B)

⇒n (A ∩ B)= 100 -80

⇒n (A ∩ B)= 20

Two events A and B are Said to be Independent, if

⇒P (A  ∩ B)=P (A) × P (B)

Probability of an event is defined as total favorable outcome divided by total possible outcome.

$\rightarrow P(A \cap B)=\frac{20}{160}\\\\P(A \cap B)=\frac{1}{8}\\\\ P(A)=\frac{40}{160}\\\\P(A)=\frac{1}{4}\\\\ P(B)=\frac{60}{160}\\\\P(B)=\frac{3}{8}\\\\P(A) \times P(B)=\frac{1}{4} \times \frac{3}{8}=\frac{3}{32}$

We see that,

⇒P (A  ∩ B)≠P (A) × P (B)

  $\rightarrow \frac{1}{8}\neq \frac{3}{32}$

so,the events are not independent.