Two events are independent if the first event has no effect on the second event.
Two events are dependent if the result of one event has an effect on the other event.
One of the most common examples of these are situations involving picking 2 items from a group of items.
If you put the item back after the first pick, it's going to be independent. It doesn't matter what you picked because you put it back and it will have no effect on the second pick. The probabilities for the first pull are the same as for the second.
If you don't put the item back, it is going to change the probabilities. You can't pick the item that has already been picked. There are fewer items to pick from. Thus it represents a dependent event.
Yes.
To determine if two events are independent or dependent, you need to analyze the relationship between the events in question. Here's a step-by-step explanation of how you can figure it out:
1. Define the two events: Clearly state what the two events are. For example, let's say event A is picking a red card from a deck of cards, and event B is picking a black card from the same deck.
2. Understand the conditions: Determine whether the events are related or have any conditions. In our example, if you replace the card back into the deck after each pick, the events are independent. However, if you do not replace the card, the events are dependent.
3. Analyze the probabilities: Calculate the probabilities of each event individually. In our example, if there are 26 red cards and 26 black cards in the deck, the probability of picking a red card on the first draw is 26/52, or 1/2. Similarly, the probability of picking a black card on the second draw (without replacement) is 26/51.
4. Determine independence or dependence:
- If the probabilities of each event remain the same regardless of the other event, the events are independent. In our example, since replacing the card after the first draw ensures that the probabilities of red and black cards remain the same for both draws, the events are independent.
- If the probability of one event changes based on the outcome of the other event, the events are dependent. In our example, without replacing the card after the first draw, the probabilities change because there are fewer cards to pick from. Therefore, the events are dependent.
Remember that independence and dependence can have different implications depending on the context. It's crucial to thoroughly understand the events and their relationship to interpret the significance appropriately.