1. Given a dependency between two events, A and B, in order to determine P(A|B) you must know both P(A) and P(B). True or False?
2. Which of the following is not a correct statement about a probability?
a. It must have a value between 0 and 1.
b. It can be reported as a decimal or a fraction.
c. A value near 0 means that the event is not likely to occur.
d. It summarizes the sample space of an experiment.
1. False. To determine P(A|B), you need to know P(A) and P(B), as well as the probability of the intersection of A and B (P(A ∩ B)). The relationship between P(A|B), P(A), P(B), and P(A ∩ B) can be defined using Bayes' theorem: P(A|B) = P(A ∩ B) / P(B), with P(A ∩ B) = P(B|A) * P(A), where P(B|A) is the conditional probability of B given A.
2. d. It summarizes the sample space of an experiment. This statement is not a correct statement about probability. Probability summarizes the likelihood of events within the sample space, but it does not directly summarize the sample space itself. The sample space refers to the set of all possible outcomes of an experiment.