Question

3. Consider a coin-die experiment: One flips a fair coin at first. If he gets a head, then he will roll a 6-sided fair die; otherwise, he will roll a 6-sided unfair die, which has probability to get i faces up (i = i, . . . , 6). If one gets a 2 faces up, what is the probability that he got a tail when he flipped the coin? 2.1

Answer 1

Let P (T) = Prob of getting tail = 1/2 P (H) = Prob of getting head = 1/2 P (i) = Prob of getting 'I' faces up = { 1/6 , for fair die 7 - i/21 , for unfair die and we need to find out P (T/2), which is: P (T intersection 2)/P (2): P (T Intersection 2) implies He got tail and so roll on un faired die implies P (T Intersection 2) = (1/2) middot (7 - 2/21) = 5/42 P (2) implies He may get '2' in two ways: - { H and then fair die rightarrow (1/2) (1/6) = 1/12 T and then un fair die rightarrow (1/2) (7 - 2/21) = 5/42 \r\n P (T/2) = (5/42)/(1/12) + (5/42) = 10/17 rightarrow answer.