Explain why choosing two socks from a drawer containing blue, red, and green socks is an example of dependent events.

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To understand why choosing two socks from a drawer containing blue, red, and green socks is an example of dependent events, we need to clarify the concept of dependent and independent events in probability.

1. **Independent Events**: Two events are independent if the occurrence of one event does not affect the occurrence of the other. For example, flipping a coin and rolling a die are independent events because the outcome of one does not influence the other.

2. **Dependent Events**: Two events are dependent if the occurrence of one event affects the occurrence of the other. This means that the outcome of the first event influences the outcome of the second event.

### Explanation of the Sock Example

When you choose the first sock from the drawer, you are reducing the total number of socks available for the second choice. Here’s how it works step by step:

- **First Sock Selection**: When you pick the first sock, you have a certain number of socks of each color (let's say $$ b $$ blue, $$ r $$ red, and $$ g $$ green). The total number of socks is $$ b + r + g $$.

- **Second Sock Selection**: After you have chosen the first sock, the total number of socks left in the drawer decreases by one. This means that the probabilities of picking a sock of each color change based on what color the first sock was. For example:
  - If you picked a blue sock first, there will be $$ b - 1 $$ blue socks left, and the total number of socks will now be $$ b + r + g - 1 $$.
  - If you picked a red sock first, there will be $$ r - 1 $$ red socks left, and again the total number of socks will be $$ b + r + g - 1 $$.
  - If you picked a green sock first, the same logic applies.

### Conclusion

Since the outcome of the first sock selection affects the probabilities of the second sock selection (the total number of socks and the number of socks of each color changes), the two events (choosing the first sock and choosing the second sock) are dependent events. The choice of the first sock directly influences the options available for the second sock, which is the hallmark of dependent events in probability.
Choosing two socks from a drawer is a dependent event because the first sock you pick affects the number and types of socks available for the second pick.

Explain why choosing two socks from a drawer containing blue, red, and green socks is an example of dependent events.

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