4.1.5. Applications of Conditional Probability

Try these first

1. 1.

   What is the definition of conditional probability?

   Hint

   Think about how one event's occurrence affects another.

2. 2.

   Write down the formula for conditional probability.

   Hint

   Recall the relationship between the intersection of A and B.

3. 3.

   What does P(A|B) signify?

   • Probability of A given B
   • Probability of B given A
   • Both A and B occur

   Hint

   Think about what condition is applied here.

4. 4.

   True or False: If P(A ∩ B) = 0, A and B are independent events.

   • True
   • False

   Hint

   Define mutual exclusivity.

5. 5.

   In a quality control scenario, suppose 3% of products are defective. If a specific test indicates a product is defective 95% of the time when it is defective and 10% of the time when it is not defective, what is the probability a product is actually defective given a test reading of defective?

   Hint

   Establish what proportions become pivotal in the context.

6. 6.

   A poll shows that 60% of voters favor candidate A. If it rains, the chance of voting increases to 80%. Calculate the conditional probability that a voter favors A given that it rains.

   Hint

   Apply the formula accordingly with conditional inputs.