Final answer:
The question asks for the calculation of probabilities for events A and B when rolling dice. Probabilities such as P(A ∩ B) require listing the specific outcomes that satisfy both events and applying probability principles.
Step-by-step explanation:
The student's question pertains to the calculation of probabilities involving two events, A and B, related to the outcomes of rolling dice. There are several components to address:
- P(A ∩ B) represents the probability of both events A and B occurring simultaneously. For dice, it could be the chance of rolling a certain sum while one die shows a specific face.
- P(A ∪ B) represents the probability of either event A or event B occurring, or both.
- P(A ∩ Bʹ) is the probability of event A happening while event B does not occur.
To find these probabilities, one would need to list the outcomes that make up each event and then apply the principles of probability theory, such as counting the number of favorable outcomes and dividing by the total number of outcomes in the sample space.
Example of calculation:
Let's say event A is the event of rolling a prime number on a six-sided die, and event B is rolling an odd number. A = {2, 3, 5} and B = {1, 3, 5}, hence A AND B = {3, 5}. To find P(A ∩ B), count the favorable outcomes that satisfy both A and B and divide by the total outcomes.