Final answer:
To find P(A AND B), we use the formula P(A OR B) = P(A) + P(B) - P(A AND B). Given P(A) = 0.37, P(B) = 0.15, and P(A or B) = 0.48, it can be calculated that P(A AND B) = 0.04.
Step-by-step explanation:
The student is asking for the probability of the intersection of events A and B, denoted as P(A AND B). From the provided probabilities, P(A) = 0.37, P(B) = 0.15, and P(A or B) = 0.48. To find P(A AND B), we can use the formula for the union of two events: P(A OR B) = P(A) + P(B) - P(A AND B).
Using the given probabilities, we can rearrange this formula to solve for P(A AND B):
- P(A OR B) = P(A) + P(B) - P(A AND B)
- 0.48 = 0.37 + 0.15 - P(A AND B)
- 0.48 = 0.52 - P(A AND B)
- P(A AND B) = 0.52 - 0.48
- P(A AND B) = 0.04
Therefore, the probability of both events A and B occurring together is 0.04.