In order for the Law of AND to work, the two events have to be independent. What

Question

In order for the Law of AND to work, the two events have to be independent. What does that mean? It means that one event does not influence the other. The fact that one event has occurred does not make the other more likely. For example, getting hurt and going to the hospital are NOT independant events. My chances of getting hit on the head by a falling tree this year are maybe 1 in a hundred, or 1%. My chances of going to the emergency room this year are maybe also 1%. So using the Law of AND, my chances of getting hit in the head would be 1% * 1% = 0.01 * 0.01 = 0.0001 = 0.01%, or one-hundreth of a percent. But in fact, IF I get hit in the head, I'm likely to want to go to the hospital for that very reason. So, the two events are NOT independent!! And my chances of getting hit in the head and going to the hospital are much bigger than 0.01%. Maybe more like 0.5% (about half the time that I get hit in the head I go to the hospital). Which of the following events are independent?

Flipping a coin once and getting tails, and flipping a coin a second time and getting heads.

The probability of being hungry and the probability of getting a snack.

Pulling one card from a deck of cards and getting a red suit (hearts or diamonds) and pulling a second card from the same deck of cards and getting a second red suit.

The probability of it raining on the same day there is a pop quiz in one of your classes.

Explanation / Answer

Flipping a coin once and getting tails, and flipping a coin a second time and getting heads. (Independent)

The probability of being hungry and the probability of getting a snack. (Dependent)

Pulling one card from a deck of cards and getting a red suit (hearts or diamonds) and pulling a second card from the same deck of cards and getting a second red suit. (Dependent)

The probability of it raining on the same day there is a pop quiz in one of your classes. (Independent)

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