Probability Theory

Step 1: Total outcomes.
When two unbiased dice are thrown, the total number of possible outcomes is the product of the number of faces on each die, which is: So, there are 36 possible outcomes.

Step 2: Favorable outcomes.
We need to find the favorable outcomes where the sum of the numbers on the two dice is 10. The possible pairs of numbers that sum to 10 are: Thus, there are 3 favorable outcomes.

Step 3: Probability.
The probability of an event is given by:

Final Answer: .

Step 1: Total outcomes.
The total number of outcomes is the number of cards in the deck, which is 52.

Step 2: Face cards.
In a deck of 52 cards, there are 3 face cards (Jack, Queen, King) in each suit. So, the total number of face cards is:

Step 3: Probability.
The probability of drawing a face card is:

Final Answer: .