Question

Thor surveyed students in the school to see what their favorite subject is. He recorded the data in the table shown.

Is favorite subject independent of grade level? Explain.

A) No, the probability of being in 9th grade is the same as the probability of being in 9th grade given you like math.

B) Yes, the probability of being in 9th grade is the same as the probability of being in 9th grade given you like math.

C) No, the probability of being in 9th grade is different from the probability of being in 9th grade given you like math.

D) Yes, the probability of being in 9th grade is different from the probability of being in 9th grade given you like math.

Answer 1

C) No, the probability of being in 9th grade is different from the probability of being in 9th grade given you like math.

Answer 2

Option: C is the correct answer.

C) No, the probability of being in 9th grade is different from the probability of being in 9th grade given you like math.

Explanation:

We are given a table as follows:

Grade English History Math Science Total

9 5 28 32 17 82

10 24 26 17 10 77

11 8 15 27 22 72

12 10 17 28 13 68

Total 47 86 104 62 299

Let P denote the probability of an event.

Let A and B be two events then they are independent if:

P(A∩B)=P(A)×P(B)

Hence,

`P(B|A)=P(B)`

Here let A be the event that the you like math.

and B be the event that you are in ninth grade.

Hence, A∩B is the event that you are in ninth grade and like math.

Hence, from table we have:

`P(A)=(104)/(299)\\\\\\P(A\bigcap B)=(32)/(299)\\\\\\P(B)=(82)/(299)\\\\\\P(B|A)=(P(A\bigcap B))/(P(A))\\\\\\P(B|A)=(32)/(104)`

As,

`P(B|A)\\eq P(B)`

Hence, the favorite subject is not independent of grade level.