40 US quarters and 10 Canadian quarters if 5 quarters are randomly picked from the bag. What is the probability of getting at least one Canadian quarter

To find the probability of getting **at least one Canadian quarter** when randomly picking 5 quarters from a bag containing 40 US quarters and 10 Canadian quarters, we can approach this using complementary probability.

### Step-by-Step Solution:

1. **Total quarters:**
   - 40 US quarters + 10 Canadian quarters = **50 quarters** in total.

2. **Complementary event:**
   The complementary event to "getting at least one Canadian quarter" is "getting no Canadian quarters." So, we first calculate the probability of picking 5 US quarters (no Canadian quarters), and then subtract that from 1.

3. **Ways to pick 5 US quarters:**
   - There are 40 US quarters, so the number of ways to choose 5 US quarters from the 40 available is:
     \[
     \binom{40}{5}
     \]
   
4. **Ways to pick 5 quarters from 50 total quarters:**
   - The total number of ways to pick any 5 quarters from the 50 total quarters is:
     \[
     \binom{50}{5}
     \]

5. **Probability of picking 5 US quarters:**
   The probability of selecting 5 US quarters (no Canadian quarters) is:
   \[
   P(\text{no Canadian quarters}) = \frac{\binom{40}{5}}{\binom{50}{5}}
   \]

6. **Probability of at least one Canadian quarter:**
   The probability of getting at least one Canadian quarter is the complement of the above:
   \[
   P(\text{at least one Canadian quarter}) = 1 - P(\text{no Canadian quarters})
   \]
   
Let me calculate this for you.The probability of getting at least one Canadian quarter when picking 5 quarters from the bag is approximately **0.6894** or **68.94%**.

Would you like more details or have any questions?

Here are some related questions:
1. What is the probability of getting exactly one Canadian quarter?
2. How does the probability change if there are only 30 US quarters and 20 Canadian quarters?
3. What is the probability of getting all 5 quarters as Canadian?
4. How would the probability change if you only pick 3 quarters?
5. What is the probability of picking at least two Canadian quarters?

**Tip:** When dealing with "at least one" probability questions, it's often easier to calculate the complement ("none") and subtract from 1.

40 US quarters and 10 Canadian quarters if 5 quarters are randomly picked from the bag. What is the probability of getting at least one Canadian quarter?

Calculate the probability of picking at least one Canadian quarter when selecting 5 quarters from a bag of 40 US quarters and 10 Canadian quarters. This detailed step-by-step solution uses combinatorics and complementary probability, suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation