Compute urn-draw probabilities and expectations

Q: Compute urn-draw probabilities and expectations

This question evaluates understanding of elementary probability concepts—dependent events, conditional probability, and expected value—using an urn model with draws without replacement.

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Question

Urn Drawing Probabilities (Without Replacement)

You have an urn with 12 balls: 5 red (R) and 7 blue (B). You draw two balls uniformly at random without replacement.

Answer the following:

(a) What is the probability of drawing at least one red ball in the two draws?

(b) Given that the first draw is blue, what is the probability that the second draw is red?

(c) What is the expected number of red balls drawn in two draws? Show your calculations.

Assume all draws are without replacement and equally likely.

Compute urn-draw probabilities and expectations

Urn Drawing Probabilities (Without Replacement)

Solution

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Compute urn-draw probabilities and expectations

Overview

Urn Drawing Probabilities (Without Replacement)

Solution

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