To calculate the probability of picking a quarter first and then a nickel without replacement, we need to follow these steps:

1. Determine the total number of coins in the set.
2. Calculate the probability of selecting a quarter in the first draw.
3. Calculate the probability of selecting a nickel in the second draw, given that a quarter has already been removed.
4. Multiply the probabilities from steps 2 and 3, as these are dependent events.

Let the number of quarters = $Q$, nickels = $N$, and total coins = $T$. Without specific numbers, we solve symbolically:

Step-by-step Formula

1. First draw: Probability of selecting a quarter: $P(\text{quarter}) = \frac{Q}{T}$

2. Second draw (after a quarter is removed): $P(\text{nickel | quarter picked}) = \frac{N}{T-1}$

3. Multiply these probabilities: $P(\text{quarter then nickel}) = P(\text{quarter}) \cdot P(\text{nickel | quarter picked}) = \frac{Q}{T} \cdot \frac{N}{T-1}$

Example Calculation

If the set contains, for instance:

• 3 quarters ($Q = 3$),
• 2 nickels ($N = 2$),
• Total coins ($T = 3 + 2 = 5$),

Then:

1. Probability of selecting a quarter first: $P(\text{quarter}) = \frac{3}{5}$

2. Probability of selecting a nickel second: $P(\text{nickel | quarter picked}) = \frac{2}{4} = \frac{1}{2}$

3. Combined probability: $P(\text{quarter then nickel}) = \frac{3}{5} \cdot \frac{1}{2} = \frac{3}{10}$

Let me know the exact number of coins if you'd like a specific solution!

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Would you like a detailed breakdown or have any questions?

Here are 5 related questions:

1. What is the probability of picking two quarters in a row without replacement?
2. How does the probability change if the first coin is replaced before the second draw?
3. What is the probability of selecting a nickel first and then a quarter?
4. How can you determine probabilities for more than two consecutive picks?
5. What happens if the set contains different types of coins, like dimes or pennies?

Tip: When dealing with "without replacement" problems, always adjust the total count of items after each selection.