Problem 1.

When a die is thrown the outcome can be any of the numbers from 1 to 6. If two dice are thrown the set of outcomes that ensure the sum is 9 is {(3, 6), (6,3), (4, 5), (5, 4)}. The total number of possible outcomes is 6*6 = 36

This gives the required probability as 4/36 = 1/9

The probability of getting 9 as the sum when 2 dice are thrown is 1/9.

Problem 2.

A standard deck of cards has 52 cards with 4 aces and 4 queens. The total number of outcomes when two cards are randomly picked is 52*51 = 2652. There are 4 ways in which the first card picked can be an ace. And there are 4 ways in which the second card can be a queen. It is important to notice that the order of picking an ace and a queen is not important here. As a result, we also have to consider the possibility of picking a queen followed by an ace. This gives the total number of ways in which an ace and a queen can be picked as 4*4 + 4*4 = 32. The required probability is 32/2652 = 8/663

When 2 cards are randomly picked from a standard deck of cards the probability of picking a queen and an ace is 8/663.