Question 7 (10pts) Sally grabs a die at random from a box containing two 4-sided dice, one 8-sided die, and one 12-sided die. All dice are fair. An m-sided dice has m sides with numbers 1, 2, ..., m. She rolls the die once and reports that the result is 7. a) What is the prior predictive probability of rolling a 7? (3pts) b) What are the posterior odds that the die has 12 sides? (3pts) c) Given the number of the first roll is 7. what is the probability that the next roll of the same grabbed die will be a 4? (4pts) Question 8 (10pts) There are registration forms for 10, 15, and 25 candidates from 3 regions. Among them, there are 3, 7, and 5 registration forms for girls, respectively. A region is randomly selected with equal probability first, then two registration forms are drawn without replacement from the region successively. a) The probability p that the first one is a girl's registration form. (4pts) b) It is known that the second drawn one is a boy's registration form, find the probability 4 that the first drawn one is from a girl. (6pts)