Math Problem Statement

answer

Let A and B be two independent events. If P(A) = 0.5, what can you say about P(A | B)?

Solution

This question involves conditional probability and independent events.

We are given that P(A)=0.5P(A) = 0.5 and that AA and BB are independent events. The question asks about P(AB)P(A \mid B), the conditional probability of AA given BB.

For independent events, the conditional probability P(AB)P(A \mid B) is equal to the unconditional probability P(A)P(A). This is because knowing whether BB has occurred does not change the likelihood of AA occurring if the two events are independent.

Thus: P(AB)=P(A)=0.5P(A \mid B) = P(A) = 0.5

The correct answer is: It is equal to .5.

Would you like further details or have any other questions?

Here are 5 related questions:

  1. How is conditional probability different from joint probability?
  2. How do you calculate conditional probability for dependent events?
  3. What does it mean for two events to be mutually exclusive?
  4. Can independent events be mutually exclusive?
  5. How would the formula for P(AB)P(A \mid B) change if AA and BB were dependent?

Tip: For independent events, the occurrence of one event does not affect the probability of the other event. Always check if events are independent before calculating conditional probabilities.

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Math Problem Analysis

Mathematical Concepts

Probability
Conditional Probability
Independent Events

Formulas

P(A | B) = P(A) for independent events

Theorems

Independence of events theorem in probability

Suitable Grade Level

College-level Probability or Advanced High School