Final answer:
For part b), P(A) = 1/6. For part c), P(B) = 5/12. For part d), P(A/B) is not given. For part e), mutual exclusivity cannot be determined. For part f), independence cannot be determined.
Step-by-step explanation:
b. The probability, P(A), of rolling either a three or four on the first roll and an even number on the second roll can be found by multiplying the individual probabilities. The probability of rolling a three or four is 2/6 = 1/3, and the probability of rolling an even number is 3/6 = 1/2. Therefore, P(A) = (1/3)*(1/2) = 1/6.
c. The probability, P(B), of the sum of two rolls being at most seven can be found by counting the favorable outcomes and dividing by the total number of possible outcomes. The favorable outcomes are {(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1)}, which is 15 outcomes. The total number of possible outcomes is 6*6 = 36. Therefore, P(B) = 15/36 = 5/12.
d. P(A/B) represents the probability of event A occurring given that event B has occurred. P(A/B) can be found using the formula P(A|B) = P(A and B) / P(B). However, the value of P(A and B) is not given in the question, so we cannot find P(A|B) without additional information.
e. To determine if events A and B are mutually exclusive, we need to check if their intersection is empty. From the given information, we do not know the values of P(A and B) and P(A) or P(B), so we cannot determine if they are mutually exclusive.
f. To determine if events A and B are independent, we need to check if the probability of one event is affected by the occurrence of the other event. From the given information, we do not have the required probabilities to determine if events A and B are independent.