You roll a pair of fair six-sided dice. The sample space of 363636 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 333?
What is P(B)P(B)P, left parenthesis, B, right parenthesis, the probability that the sum of the dice is 888?
What is P(A\text{ 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 333 and the sum of the dice is 888?
What is P(B\text{ | }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 888 given that the first die is a 333?
Is P(B\text{ | }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?