A bag contains 38 U.S. quarters and twelve Canadian quarters. (The coins are identical in size.) If six quarters are randomly picked from the bag, what is the probability of getting at least one Canadian quarter? (Round your answer to one decimal place.)
 % not 83.7 or 91.2, or 92.2 so what is the answer

To solve this problem, we need to calculate the probability of picking at least one Canadian quarter when six quarters are drawn from the bag. We can approach this by first finding the probability of the complementary event: picking no Canadian quarters at all (i.e., picking only U.S. quarters), and then subtracting this probability from 1.

### Step 1: Define the total quarters and probabilities
- Total quarters = 38 (U.S. quarters) + 12 (Canadian quarters) = 50 quarters.
  
### Step 2: Probability of picking only U.S. quarters
Let's calculate the probability of picking 6 U.S. quarters in a row, without picking any Canadian quarters.

The probability of picking only U.S. quarters is calculated by choosing 6 quarters from the 38 U.S. quarters without choosing any from the 12 Canadian quarters. 

The probability can be computed using the hypergeometric probability formula, but it's simpler to calculate it step by step as follows:

\[
P(\text{no Canadian quarters}) = \frac{\binom{38}{6}}{\binom{50}{6}}
\]

### Step 3: Calculate the binomial coefficients

Let's calculate these values:

- \(\binom{38}{6}\): Number of ways to choose 6 U.S. quarters from 38.
- \(\binom{50}{6}\): Total ways to choose 6 quarters from 50. 

Let’s compute this: 

The probability of getting at least one Canadian quarter when six quarters are randomly picked from the bag is **82.6%**.

### Would you like more details or have any questions?

Here are some related questions:
1. How do you calculate binomial coefficients?
2. What is the hypergeometric distribution, and how is it used in probability?
3. How would the probability change if the number of Canadian quarters was increased?
4. What if you wanted to find the probability of exactly two Canadian quarters?
5. How does the rounding affect probability calculations?

**Tip:** To solve "at least one" problems, it's often easier to calculate the probability of the complementary event and subtract it from 1.

A bag contains 38 U.S. quarters and twelve Canadian quarters. (The coins are identical in size.) If six quarters are randomly picked from the bag, what is the probability of getting at least one Canadian quarter? (Round your answer to one decimal place.)

Learn how to calculate the probability of picking at least one Canadian quarter from a bag containing 38 U.S. quarters and 12 Canadian quarters. This problem covers key probability concepts, including combinatorics and hypergeometric distribution. Suitable for students in Grades 9-12.

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