Financial Risk Manager Part 1

Explanation:

Events are considered independent if the occurrence of one event does not affect the probability of the other event occurring.

• Option A (Rolling a die; rolling another die): These are independent events because the outcome of one die roll does not affect the outcome of the other die roll.

• Option B (Flipping a coin; flipping a coin): These are independent events because the outcome of one coin flip does not affect the outcome of another coin flip.

• Option C (Rolling a die; flipping a coin): These are independent events because these are completely different random processes that don't influence each other.

• Option D (Drawing a card; drawing another card from the same deck): These are NOT independent events. When you draw a card from a deck without replacement, the composition of the deck changes. The probability of drawing a particular card on the second draw depends on what card was drawn first. For example, if you draw an Ace on the first draw, there are only 3 Aces left in the deck of 51 cards for the second draw, changing the probability from 4/52 to 3/51.

This question tests the fundamental concept of independent vs. dependent events in probability theory, which is essential for understanding statistical relationships in financial risk modeling.