Probability Modeling and Conditioning Lab

Retrieval Prompts

1. State the difference between an outcome, an event, and a random variable.
2. Write the complement rule and the addition rule for two events.
3. State the definition of conditional probability from memory.
4. State Bayes' rule and explain each term in words.
5. State the difference between disjointness and independence.

Compare and Distinguish

Separate these pairs clearly:

• equally likely outcomes versus merely several possible outcomes
• P(A | B) versus P(B | A)
• disjoint events versus independent events
• event union versus event intersection

Common Mistake Check

For each statement, identify the error:

1. "There are three possible sums when two coins are flipped: 0, 1, 2, so each has probability 1/3."
2. "The test is 99% accurate, so a positive result means a 99% chance the disease is present."
3. "Events that cannot happen together are independent."
4. "At least one failure means add the failure probabilities directly."

Mini Application

Do all four tasks for each scenario:

1. define the sample space
2. define the event(s)
3. identify whether complement or conditioning is useful
4. explain whether equal-likelihood reasoning is legitimate

Scenarios:

1. two cards drawn without replacement, probability both are aces
2. one child is known to be a girl, probability both children are girls
3. system alert fires when the base-rate of failures is very low

Evidence Check

This page is complete only if you can explain the model in sentences before you compute any probability.