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,
[tex]P(B|A)=P(B)[/tex]
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:
[tex]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}[/tex]
As,
[tex]P(B|A)\neq P(B)[/tex]
Hence, the favorite subject is not independent of grade level.
