6)You are given the information that P(A) =0.30 and P(B) =0.40 (a) Do you have enough information to compute P(A or B)? Explain.(events A and B are mutually b) If you know that events A and B are mutually exclusive , do you have enough information to compute P(A or B)? Explain.
8) For a class activity, your group has been assigned the task of generating a quiz question that requires use of formula for conditional probability to compute P(B/A). Your group comes up with the following question” “If P(A and B) -0.40 and P(A) =0.20, what is the value of P(B/A)?” What is wrong with this question? Hint: Consider the answer you get when using the correct formula, P(B/A) = P(A and B)/P(A).
The value of P(B/A) = 0
P(B/A) = 0
P(A/B) = .40/.20 = 0.2
6a) No, we do not have enough information to compute P(A or B) because we do not know the probability of the events occurring together or the probability of their intersection (P(A and B)). To calculate P(A or B), we need to know both the individual probabilities (P(A) and P(B)) and the probability of their intersection.
6b) If events A and B are mutually exclusive, it means that they cannot occur at the same time. In this case, since they are mutually exclusive, we know that P(A and B) = 0. Therefore, we do have enough information to compute P(A or B). When events are mutually exclusive, the formula for P(A or B) simplifies to P(A) + P(B).
6) (a) To compute P(A or B), you would need to have information about the relationship between events A and B, specifically whether they are dependent or independent. If A and B are independent events, you can use the formula P(A or B) = P(A) + P(B) - P(A and B). However, without knowing whether events A and B are dependent or independent, it is not possible to compute P(A or B) with the given information.
(b) If events A and B are mutually exclusive, it means that they cannot occur at the same time (i.e., if A happens, B cannot happen, and vice versa). In this case, knowing the information that events A and B are mutually exclusive is sufficient to compute P(A or B). When events are mutually exclusive, the formula to compute P(A or B) simplifies to P(A) + P(B), as there is no overlap or intersection between the events.
8) The issue with the provided quiz question is that there is an error in the formula for conditional probability. The correct formula for P(B/A) is P(A and B) / P(A), as stated in the hint. However, in the question, it states P(A and B) = 0.40 and P(A) = 0.20, which are the incorrect values. This inconsistency results in an incorrect calculation when using the correct formula. To fix the question, the values for P(A and B) and P(A) should be accurately provided.