Two events are said to be independent when the occurrence of one does not affect the occurrence of the other. Conversely, if the occurrence of one affects the occurrence of the other, they events are dependent.
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Two events are said to be independent when the occurrence of one does not affect the occurrence of the other. Conversely, if the occurrence of one affects the occurrence of the other, they events are dependent. First, we will give one example of each type of event. Then we will describe how the examples differ.
Independent Events
Suppose that we have a deck of shuffled cards and a standard die. Now, consider the event of getting a king from the cards and 1 on the die.
The probability of getting a king on the cards is 452 and the probability of getting 1 on the die is 16. Additionally, note that the result of the card does not affect the result of the die and vice versa. Therefore, the events are independent.
Dependent Events
Again, suppose that we have a deck of shuffled cards and a standard die. Suppose that after rolling a die, the square of the outcome of the die is the number of cards removing randomly from the deck. Now, consider the event of getting a four on the die and a king on the cards.
Note that the removed cards could be 1, 2, 3, or the 4 kings. Since removing cards after rolling the die affects the probability of getting a king on the deck, we have dependent events.
How the Examples Differ
Now, let's point the differences between our events.
In the first event, what happened on the die does not affect the outcome of the cards. Conversely, in the second experiment, the outcome of the die directly affect the outcome of the cards.
In the first event, the order of the individual events does not matter. On the other hand, in the second event we must first roll the die and then take a card from the deck.
Note that these are only some differences. However, because there are many possible examples of dependent and independent events, these differences may vary.
