Two events are considered to be independent of each other when the probability that one event occurs in no way affects the probability of the other event occurring. Since some students have green eyes and brown hair, some have green eyes and not brown hair, and not green eyes and brown hair, therefore the two events are not independent. To say, they are dependent.
We can prove this mathematically by:
P(A∩B)=P(A) * P(B) --> If equal, then independent
Where A = green eyes
B = brown hair
From the table:
P(A∩B) = 16/50 (16 out of 50 has green eyes and brown hair)
P(A) = 28/50 (28 out of 50 has green eyes)
P(B) = 30/50 (30 out of 50 has brown hair)
16/50 = (28/50) * (30/50)
16/50 = 840 / 2500 (NOT TRUE)
Answer:
Not independent
