4.1.1. Definition

Try these first

1. 1.

   Define conditional probability in your own words.

   Hint

   Think of it as narrowing down the possibilities.

2. 2.

   What does the formula P(A|B) represent?

   Hint

   Focus on the relationships between the events.

3. 3.

   What does P(A|B) represent?

   • The probability of A given B
   • The probability of B given A
   • The joint probability of A and B

   Hint

   Think about how one event affects the other.

4. 4.

   True or False: If P(B) = 0, we can calculate P(A|B).

   • True
   • False

   Hint

   Consider the implications of dividing by zero.

5. 5.

   A medical test has a 95% accuracy for a disease found in 1% of the population. If someone tests positive, what is the probability they actually have the disease?

   Hint

   Break it down step by step using provided formulas.

6. 6.

   In a factory, 70% of incidents are due to machinery failure, 10% due to human error, and 20% due to external factors. If an incident occurs, what is the probability it was due to machinery failure?

   Hint

   Consider the weighting of each factor when calculating probability across all incidents.