📚 Topic Summary
Conditional probability deals with the likelihood of an event occurring given that another event has already happened. It's written as $P(A|B)$, which means "the probability of event A happening, given that event B has already happened." Independence, on the other hand, means that the occurrence of one event doesn't affect the probability of the other. If events A and B are independent, then $P(A|B) = P(A)$. In essence, one event doesn't give you any new information about the likelihood of the other.
This worksheet helps you practice applying these concepts through vocabulary, fill-in-the-blanks, and critical thinking exercises.
🧠 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Conditional Probability |
A. Events where the outcome of one doesn't affect the other. |
| 2. Independent Events |
B. The probability of an event given that another has occurred. |
| 3. Sample Space |
C. An event that is certain to happen. |
| 4. Certain Event |
D. The set of all possible outcomes of an experiment. |
| 5. Probability |
E. A number expressing the likelihood of occurrence of an event. |
(Match: 1-B, 2-A, 3-D, 4-C, 5-E)
✍️ Part B: Fill in the Blanks
Complete the following sentences:
If events A and B are _______, then $P(A|B) = P(A)$. Conditional probability is denoted as P(A|B), which reads "the probability of A _______ B." The _______ space includes all possible outcomes of an experiment.
(Answers: independent, given, sample)
🤔 Part C: Critical Thinking
Explain, in your own words, how conditional probability differs from the probability of independent events. Provide a real-world example to illustrate your explanation.