Consider the following populations and samples. For each try to decide which po

Consider the following populations and samples.  For each try to decide which population the sample was more likely to have been drawn from.
a)  A standard deck (population 1) has 52 cards, one copy of Duece (2) through Ace for each of the four suits ( ♥, ♦, ♣, ♠); a Pinochle deck (population 2) has 48 cards, two from each of the four suits, 9 through Ace (9,10,J,Q,K,A).  If you were dealt 9♥, 10♠, J♣, K♠, A♥ (our sample), which deck (population) is this hand more likely to have come from?  How certain do you feel about your choice?


b)  At the local game store you pick up two 6-sided dice.  One die is a "true" die, with which the chances of rolling a 1, 2, 3, 4, 5, or 6 are all equivalent.  The other die is a "loaded" die, that has been weighted so that the 1 happens very infrequently, the 6 occurs more frequently than usual, and the 2, 3, 4, & 5 occur at their normal rates.  The two dice look the same and you forget which is which.  So you decide to pick one of them and roll it 6 times (our sample).  Suppose that your sample roll is: 1, 1, 3, 2, 6, 2.  Which die do you think you selected, the "true" die or the "loaded" die? How certain do you feel about your choice?