We can solve this problem using the concept of conditional probability because you're selecting coins without replacement. Let's break it down:

Step 1: Determine the total number of coins in the jar

You have:

• 5 pennies
• 28 dimes
• 17 nickels
• 29 quarters

So, the total number of coins is:

$5 + 28 + 17 + 29 = 79$

Step 2: Probability of selecting a quarter first

The probability of selecting a quarter on the first draw is the number of quarters divided by the total number of coins:

$P(\text{quarter first}) = \frac{29}{79}$

Step 3: Probability of selecting a nickel second

After you select a quarter, you don't replace it, so there are now 78 coins left in the jar. The number of nickels remains 17. Thus, the probability of selecting a nickel after having already selected a quarter is:

$P(\text{nickel second | quarter first}) = \frac{17}{78}$

Step 4: Multiply the probabilities

Since these events are sequential and without replacement, the overall probability is the product of these two probabilities:

$P(\text{quarter and then nickel}) = \frac{29}{79} \times \frac{17}{78}$

Let's calculate this:

$P(\text{quarter and then nickel}) = \frac{29 \times 17}{79 \times 78} = \frac{493}{6162} \approx 0.07998$

Final Answer:

The probability that you grab a quarter first and then a nickel is approximately 0.0800 (rounded to four decimal places).

Do you want further details or have any questions?

Here are 5 related questions to expand on the topic:

1. What is the probability of grabbing a penny and then a dime without replacement?
2. How would the probability change if the coins were replaced after each selection?
3. What is the probability of grabbing two quarters in a row without replacement?
4. What is the probability of selecting two coins of the same type in a row (e.g., two dimes)?
5. How would the total probability change if the jar also contained 10 half-dollars?

Tip: Always be careful with "without replacement" problems, as the total number of objects decreases after each selection, changing the probabilities.