Details for Example 6.7.1. You got RRW.

(a) Calculate the posterior probabilities P₁ for each of the dice.

(b) Find p = P₁(R), the probability that the next observation is R.

(c) If you have sampling with replacement, where the alternatives are red (R) and white (W), and p = P₁(red) from the above, what is then P(RRRRR)?

(d) Find p = P₁(RRRRR), the probability that the next five observations are RRRRR.

(e) Why are the probabilities in the two die questions different?

Example 6.7.1

Let us just change perspective for a moment. Instead of being one of the players, we are now Games master. We picked a new die this time, and since we have Games master’s privileged viewpoint, we know it is a D₁₀. With its 4 red and 6 white sides, P(R) = 0.4 and P(W) = 0.6, and the probability of a given sequence S of k reds and l whites is P(S) = 0.4^k0.6^l.