Suppose you are given either a fair dice or an unfair dice (6-sided). you have no basis for considering either dice more likely before you roll it and observe an outcome. for the fair dice, the chance of observing “3” is 1/6. for the unfair dice, the chance of observing “3” is 1/3. after rolling the unknown dice, you observe the outcome to be 3. what is the new probability that the die you rolled is fair

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.