Quantitative Finance
# Probability Theory

How many 4 -digit positive integers have 2 or more zeroes?

Alice and Carla are playing a dice game. Here's how it works:

- Each person rolls a die, and the highest number rolled of the two is recorded.
- If the highest number rolled is a 1, 2, 3 or 4, Alice wins.
- If the highest number rolled is a 5 or a 6, Carla wins.

On average, who is more likely to win: Alice, Carla, or are the probabilities equal?

1% of people have a rare cancer, and there is a test for this cancer which is "90% accurate"; that is:

If you have the cancer there is a 90% chance the test will be positive.

If you don't have the cancer there is a 90% chance the test will be negative.

If you take the test and test positive, what is the approximate probability that you have the cancer?

A restaurant offers 5 choices of appetizer, 10 choices of the main course and 4 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming that all food choices are available, how many different possible meals does the restaurant offer?

Note: When you eat a course, you only pick one of the choices.