Which are independent events? check all that apply. rolling a number cube twice picking 2 marbles from a bag, without replacement choosing a meal/drink combination flipping a coin four times picking 2 cards from a deck, without replacement

Explanation:

Two or more events are independent of each other if the occurrence of one is not affected by the occurrence of the other.

1) Rolling a number cube twice

When you roll a number cube the outcome of the first roll does not change the possible outcomes of the second roll, so rolling a number cube twice represent indepent events.

Assume, the outcome of the first roll is a 5. The outcome of the next roll can still be 1, 2, 3, 4, 5, or 6, as much as wheter the outcome of the first roll would have been any other number.

2) Picking 2 marbles from a bag, without replacement

Since after picking the first marble you do not replace it, the outcome of the second pick will have different probabilities depending on the marble that was first picked up, so these are dependent events.

Assume the bag has one blue marble, one red marble and one yellow marble.

If you pick a blue marble the first time, the next time you cannot pick a blue one, and the probabilities of picking a red or yellow marble will be greater. So, it is clear, that occurrence of one event modify the occurrence of other event.

3) Choosing a meal/drink combination

These are independent events, because the choice of a meal will not change the choice of a drink (assuming no restrictions are impossed).

Assume there are three different meals: chicken, hot dog, and hamburgers, and there are two different drinks: juice or soda.

The fact of choosing chicken, hot dog, hamburger, does not change the probabilities of choosing juice or soda. Thus, the occurrence of one event does not modify the occurrence of the other.

4) Flipping a coin four times

Flipping a coing four times are independent events, because every time that you flip the coing the probability of seing tail or head is the same.

Each time the probability of getting tail or head is 1/2, no matter what the outcome of the previous flip be.

5) Picking 2 cards from a deck, without replacement

Picking two cards from a deck, without replacement, are dependent events, because the outcome of the second card will depend on the outcome of the first card.

If after drawing the first card it would be replaced, the events were independent, because the second time the outcomes will have the same probabilities, i.e. the occurence of one event would not change the occurrence of the second event.

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