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Answer: Our required probability is 0.83.
Step-by-step explanation:
Since we have given that
Number of dices = 2
Number of fair dice = 1
Probability of getting a fair dice P(E₁) =
Number of unfair dice = 1
Probability of getting a unfair dice P(E₂) =
Probability of getting a 3 for the fair dice P(A|E₁)=
Probability of getting a 3 for the unfair dice P(A|E₂) =
So, we need to find the probability that the die he rolled is fair given that the outcome is 3.
So, we will use "Bayes theorem":
Hence, our required probability is 0.83.