Event a is rolling a five on a six sided die and event b is rolling an odd number on the same die. are the events dependent or independent, why?

No, they are not independent. The two events are dependent events.




A = event of rolling a five 
B = event of rolling an odd number

P(A) = (number of ways to roll a five)/(number of outcomes total)
P(A) = 1/6
P(B) = (number of ways to roll an odd number)/(number of outcomes total)
P(B) = 3/6
P(B) = 1/2

P(A and B) = (number of ways to roll an odd number AND five at the same time)/(number of outcomes total)
P(A and B) = 1/6

If A and B were independent, then P(A and B) = P(A)*P(B) would be true. Let's see if it is or not

P(A and B) = P(A)*P(B)
1/6 = (1/6)*(1/2)
1/6 = 1/12

The result is false, so P(A and B) = P(A)*P(B) isn't true
This means that A and B are dependent events

If we know B has happened, then that changes the probability of A
If we know A has happened, then B is automatically true (since 5 is odd). I.e, P(B|A) = 1