Question

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

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

Answer:

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.

Step-by-step 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:

$P(A)=\dfrac{104}{299}\\\\\\P(A\bigcap B)=\dfrac{32}{299}\\\\\\P(B)=\dfrac{82}{299}\\\\\\P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\\\P(B|A)=\dfrac{32}{104}$

As,

$P(B|A)\neq P(B)$

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