Compute urn-draw probabilities and expectations
Company: MathWorks
Role: Software Engineer
Category: Statistics & Math
Difficulty: easy
Interview Round: Take-home Project
An urn contains 5 red and 7 blue balls. You draw two balls uniformly at random without replacement.
(a) What is the probability of drawing at least one red?
(b) Given that the first draw is blue, what is the probability the second draw is red?
(c) What is the expected number of red balls drawn in two draws? Show calculations.
Quick Answer: This question evaluates understanding of elementary probability concepts—dependent events, conditional probability, and expected value—using an urn model with draws without replacement.