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

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is Conditional Probability?

πŸ’‘ Hint: Think about the probability of A in the context of B.

Question 2

Easy

If the probability of event B is 0.4, what does this imply about calculating P(A|B)?

πŸ’‘ Hint: Focus on the condition here.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

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)

πŸ’‘ Hint: Remember to consider what the condition is referring to.

Question 2

True or False: If A and B are independent, then P(A|B) equals P(A).

  • True
  • False

πŸ’‘ Hint: Think about what independence means.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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?

πŸ’‘ Hint: Break down the error probabilities into parts and apply.

Question 2

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?

πŸ’‘ Hint: Draw out the sample space considering the conditions.

Challenge and get performance evaluation