Answer:
1 / 8 is not equal to 3 / 32
Explanation:
Total number of Students in the class =160
Out of which,
Number of honor students = 40
Number of Athletes = 60
The probability of the event "honor student" is: 40/160=1/4 P(A)
The probability of the event "athlete student" is: 60/160=3/8 P(B)
Two events A and B are Said to be Independent, if
⇒P (A ∩ B)=P (A) × P (B)
Total Number of students in the class - n (A ∪ B)= 80
180=n(A∪B)
⇒n (A ∪ B)=80
⇒80= 40 +60 - n(A ∩ B)
⇒n (A ∩ B)= 20
P (A ∩ B) = 20/160=1/8
Lets check: P (A ∩ B)=P (A) × P (B)

