Answer:
P(A) = 1/6
P(B) = 5/36
P(A and B) = 1/36
P(B | A) = 1/6
P(B) is different of P(B | A). As they are different, we have that A and B are DEPENDENT events.
Step-by-step explanation:
As one die has six numbers, the probability of the first die being a 3 is 1/6, because there is one number 3 in the six numbers of the dice:
P(A) = 1/6
The dice can have a sum of 8 in the following pair of values:
(2,6), (3,5), (4,4), (5,3), (6,2)
So there are 5 possibilities among the total 36, so P(B) = 5/36
The probability of the first die being 3 and the sum being 8 only happens in one pair of values:
(3,5)
So the probability P(A and B) is 1/36
The probability of the sum being 8 given that the first number is 3 is the probability of having a 5 in the second die, so it is one possibility among 6:
P(B | A) = 1/6
P(B) = 5/36 and P(B | A) = 1/6, so we have that P(B) is different of P(B | A). As they are different, we have that A and B are DEPENDENT events.
