points) A gambler has a fair (F) six-sided die (with face values 1,2,3,4,5,6) an

Question

points) A gambler has a fair (F) six-sided die (with face values 1,2,3,4,5,6) and a biased (B) die (with face values 2,2,4,4,4,6) in her chosen) and proceeds to roll it and then shows you only the value facing up. pocket. She selects one of the dice at random(both are equally likely to be a) After she rolls it once, you see the value 2. What is the probability P, that it is the fair die F? Derive the answer even if you think that it is an intuitive answer (rare case). (decimal number) ANSWER: Pa b) After she rolls it one more time, you see the value 4. Now what is the probability Ps that it is the fair die F? Derive the answer even if you think that it is an intuitive answer (rare case).

Explanation / Answer

a) There are three cases where a '2' can come. They are (i) one '2' on a fair die and (ii) two '2' on biased die.

So, the probability that the value '2' is of fair die is PA = 1/3 = 0.33.

b) There are four cases where a '4' can come. They are (i) one '4' on a fair die and (ii) three '4' on biased die.

So, the probability that the value '4' is of fair die is PB = 1/4 = 0.25.

c) There are two cases where a '6' can come. They are (i) one '6' on a fair die and (ii) one '6' on biased die.

So, the probability that the value '6' is of fair die is PC = 1/2 = 0.5.

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