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

- 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?

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

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