4.1.4. Solved Examples

Try these first

1. 1.

   What is the formula for conditional probability?

   Hint

   Think about how we define one event in relation to another.

2. 2.

   If P(A) = 0.2 and P(B) = 0.5 with P(A ∩ B) = 0.1, what is P(A|B)?

   Hint

   Use the conditional probability formula.

3. 3.

   What is the conditional probability of A given B?

   • P(A|B) = P(A ∩ B)/P(B)
   • P(A|B) = P(B ∩ A)/P(A)
   • P(A|B) = P(B)/P(A ∩ B)

   Hint

   Recall the definition of conditional probability.

4. 4.

   If two events A and B are independent, P(A|B) can be expressed as?

   • True
   • False

   Hint

   Think about the nature of independent events.

5. 5.

   A factory produces defective items at 5%. If an inspector checks 10 items, what is the probability that at least one item is defective?

   Hint

   Use the complement rule effectively.

6. 6.

   In a study, 30% of individuals smoke. If 40% of smokers and 10% of non-smokers develop lung cancer, find the probability an individual has lung cancer.

   Hint

   Ensure clear distinctions in smoker and non-smoker probabilities.