Practice Partial Differential Equations (4) - Conditional Probability - Mathematics - iii (Differential Calculus) - Vol 3

Practice: Partial Differential Equations

Lesson 4Conditional Probability

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9 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is Conditional Probability?
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Think about the probability of A in the context of B.
Question 2.
If the probability of event B is 0.4, what does this imply about calculating P(A|B)?
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Focus on the condition here.
3Question 3.
What is the formula for Conditional Probability?
- P(A|B) = P(A ∩ B) / P(B)
- P(A|B) = P(B) / P(A)
- P(A|B) = P(A) + P(B)
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Remember to consider what the condition is referring to.
4Question 4.
True or False: If A and B are independent, then P(A|B) equals P(A).
- True
- False
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Think about what independence means.
Question 5.
In a factory, 70% of the time a machine operates without errors. Consider a scenario where 90% of the errors are due to programming issues (P(E|P) = 0.9) and 10% are mechanical (P(E|M) = 0.1). If a machine fails, what is the probability that it was due to programming issues?
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Break down the error probabilities into parts and apply.
Question 6.
Two fair coins are flipped. What is the condition probability that at least one coin is heads, given that one of them is known to be heads?
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Draw out the sample space considering the conditions.

5 more questions in this section. Enroll free to practise them all.