Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following:

5
 Pennies	28
 Dimes
17
 Nickels	29
 Quarters

What is the probability that you reach into the jar and randomly grab a quarter and then, without replacement, a nickel? Express your answer as a fraction or a decimal number rounded to four decimal places.

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.

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following:
5 Pennies, 28 Dimes, 17 Nickels, 29 Quarters. What is the probability that you reach into the jar and randomly grab a quarter and then, without replacement, a nickel? Express your answer as a fraction or a decimal number rounded to four decimal places.

Find the probability of selecting a quarter and then a nickel from a jar containing 5 pennies, 28 dimes, 17 nickels, and 29 quarters. Learn how to apply conditional probability and the multiplication rule to solve problems involving selections without replacement. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation