You roll a pair of fair six-sided dice. The sample space of 36 possible outcomes is shown below. Based on this information, answer the following questions.
What is P(A)P(A)P, left parenthesis, A, right parenthesis, the probability that the first die is a 3?

What is P(B)P(B)P, left parenthesis, B, right parenthesis, the probability that the sum of the dice is 8?

What is P(A and B)P(A and B)P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, the probability that the first die is a 3 and the sum of the dice is 8?

What is P(B | A)P(B | A)P, left parenthesis, B, start text, space, vertical bar, space, end text, A, right parenthesis, the conditional probability that the sum of the dice is 8 given that the first die is a 3?

Is P(B | A)=P(B)P(B | A)=P(B)P, left parenthesis, B, start text, space, vertical bar, space, end text, A, right parenthesis, equals, P, left parenthesis, B, right parenthesis? Are the events AAA and BBB independent?