One of two dice is chosen at random. Die is fair. Die is loaded so that . The chosen die is rolled twice and shows a 6 both times. What is the probability that it was die ?

Answer and explanation

Correct answer: D.

  1. Step 1: Define prior probabilities: each die has prior probability .
  2. Step 2: Calculate likelihoods of rolling two consecutive sixes: for fair die , ; for loaded die , .
  3. Step 3: Apply Bayes' theorem: .
Answer
.

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