4.1. Conditional Probability

Try these first

1. 1.

   What is the formula for conditional probability?

   Hint

   Think about the relationship between A and B.

2. 2.

   Give an example of mutually exclusive events.

   Hint

   Think about outcomes that cannot co-occur.

3. 3.

   What does P(A|B) represent?

   • Probability of A given B
   • Probability of B given A
   • Joint probability of A and B

   Hint

   Think about how we define conditional probabilities.

4. 4.

   If P(A) = 0.2 and P(B) = 0.3 are independent, what is P(A ∩ B)?

   • 0.05
   • 0.06
   • 0.08

   Hint

   Remember the product rule for independent events.

5. 5.

   In a factory, 80% of machinery is working. If a machine is selected and found to be faulty (20% failure rate), what is the conditional probability that another machine from the same batch is also faulty?

   Hint

   Analyze the relationship and use previous probabilities.

6. 6.

   If a test for a rare disease is 92% accurate and the prevalence in the population is 0.5%, what is the probability someone who tests positive actually has the disease?

   Hint

   Set up the prior probabilities accurately to derive the final conditional probability.