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)=(20)/(160)\\\\P(A \cap B)=(1)/(8)\\\\ P(A)=(40)/(160)\\\\P(A)=(1)/(4)\\\\ P(B)=(60)/(160)\\\\P(B)=(3)/(8)\\\\P(A) * P(B)=(1)/(4) * (3)/(8)=(3)/(32)`

We see that,

⇒P (A ∩ B)≠P (A) × P (B)

`\rightarrow (1)/(8)\\eq (3)/(32)`

so,the events are not independent.