Compute two conditional probability scenarios

Q: Compute two conditional probability scenarios

This question evaluates a candidate's understanding of conditional probability, Bayesian reasoning for posterior inference, and combinatorial counting in finite-sample probabilities.

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Question

Probability — Two-Part Question

Solve both parts. Show formulas and provide final numeric values.

Part A — Coin Type Given HHH

A box has 5 coins: 3 fair coins (P(H)=0.5 per flip) and 2 double-headed coins (always heads).
You pick one coin uniformly at random, flip it three times, and observe H, H, H.
Compute P(double-headed | 3 heads observed).

Part B — Urn Colors

An urn contains 5 red, 4 blue, and 3 green balls (total 12).
You draw 3 balls without replacement.
What is the probability that exactly two distinct colors appear and at least one ball is red?

Compute two conditional probability scenarios

Probability — Two-Part Question

Part A — Coin Type Given HHH

Part B — Urn Colors

Solution

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Compute two conditional probability scenarios

Overview

Probability — Two-Part Question

Part A — Coin Type Given HHH

Part B — Urn Colors

Solution

Comments (0)