Answer:
No, the events "brown hair" and "brown eyes" are not independent.
Explanation:
The table that represents the hair and eye colors of thirty students of the fifth grade are given in table as:
Brown hair Blonde hair Total
Green eyes 9 6 15
Brown eyes 10 5 15
Total 19 11 30
No, the events "brown hair" and "brown eyes" are not independent.
Since, two events A and B are said to be independent if:
P(A∩B)=P(A)×P(B)
where P denotes the probability of an event.
Here we have:
A= students having brown hair.
B= students having brown eyes.
A∩B= students having both brown hair and brown eyes.
Now,
P(A)=19/30 (ratio of addition of first column to the total entries)
P(B)=15/30 ( ratio of addition of second row to the total entries)
Also,
P(A∩B)=10/30
Now as:
P(A∩B) ≠ P(A)×P(B)
Hence, the two events are not independent.