ababg contain 8 marbles and 12 blue marbles. john selects two marbles with replacements

Let's analyze the situation step by step:

1. **Total Marbles:**
   - There are 8 red marbles and 12 blue marbles.
   - Total number of marbles = 8 (red) + 12 (blue) = 20 marbles.

2. **Selection with Replacement:**
   - Since John is selecting two marbles with replacement, the total number of marbles remains the same after each selection.

3. **Calculating Probabilities:**

   - **Probability of Selecting a Red Marble:**
     \[
     P(\text{Red}) = \frac{8}{20} = \frac{2}{5}
     \]

   - **Probability of Selecting a Blue Marble:**
     \[
     P(\text{Blue}) = \frac{12}{20} = \frac{3}{5}
     \]

   - Since the selections are with replacement, the probability of each event does not change after the first selection.

4. **Possible Outcomes:**

   - **Red, Red:** 
     \[
     P(\text{Red, Red}) = P(\text{Red}) \times P(\text{Red}) = \frac{2}{5} \times \frac{2}{5} = \frac{4}{25}
     \]

   - **Red, Blue:** 
     \[
     P(\text{Red, Blue}) = P(\text{Red}) \times P(\text{Blue}) = \frac{2}{5} \times \frac{3}{5} = \frac{6}{25}
     \]

   - **Blue, Red:** 
     \[
     P(\text{Blue, Red}) = P(\text{Blue}) \times P(\text{Red}) = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}
     \]

   - **Blue, Blue:** 
     \[
     P(\text{Blue, Blue}) = P(\text{Blue}) \times P(\text{Blue}) = \frac{3}{5} \times \frac{3}{5} = \frac{9}{25}
     \]

These probabilities cover all possible outcomes when John selects two marbles with replacement.

Would you like more details or have any specific questions?

---

Here are 5 related questions:

1. What is the probability of selecting at least one blue marble?
2. How does the probability change if the selections are without replacement?
3. What is the expected number of blue marbles in two draws?
4. How would the outcome probabilities change if the number of red and blue marbles were equal?
5. Can you calculate the variance in the number of blue marbles selected in two draws?

**Tip:** When dealing with probabilities, always ensure whether the events are independent (with replacement) or dependent (without replacement) as it significantly affects the calculations.

Understand the probability of selecting red and blue marbles with replacement. Learn how to calculate probabilities for different outcomes when selecting two marbles from a set of 8 red and 12 blue marbles. Explore step-by-step solutions and calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation