Practice Solved Examples (4.1.4) - Conditional Probability - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What is the formula for conditional probability?
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Think about how we define one event in relation to another.
Question 2.
If P(A) = 0.2 and P(B) = 0.5 with P(A ∩ B) = 0.1, what is P(A|B)?
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Use the conditional probability formula.
3Question 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)
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Recall the definition of conditional probability.
4Question 4.
If two events A and B are independent, P(A|B) can be expressed as?
- True
- False
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Think about the nature of independent events.
Question 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?
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Use the complement rule effectively.
Question 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.
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Ensure clear distinctions in smoker and non-smoker probabilities.

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