Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Sure, let's break this problem down step-by-step.
### Step 1: Determine the Total Number of Marbles
First, we need to understand the composition of the marbles in the bag:
- Red marbles: 3
- Yellow marbles: 2
- Green marbles: 3
So, the total number of marbles in the bag is:
[tex]\[ 3 + 2 + 3 = 8 \][/tex]
### Step 2: Probability of Drawing the First Green Marble
To find the probability of drawing a green marble first, we look at the number of green marbles and the total marbles:
[tex]\[ \text{Probability of drawing first green marble} = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{3}{8} = 0.375 \][/tex]
### Step 3: Probability of Drawing the Second Green Marble
After drawing one green marble, there are now 2 green marbles left and a total of 7 marbles remaining in the bag.
[tex]\[ \text{Probability of drawing second green marble} = \frac{\text{Remaining green marbles}}{\text{Remaining total marbles}} = \frac{2}{7} \approx 0.2857 \][/tex]
### Step 4: Probability of Drawing a Yellow Marble on the Third Draw
After drawing two green marbles, there are 2 yellow marbles left and a total of 6 marbles remaining in the bag.
[tex]\[ \text{Probability of drawing third yellow marble} = \frac{\text{Remaining yellow marbles}}{\text{Remaining total marbles}} = \frac{2}{6} = \frac{1}{3} \approx 0.3333 \][/tex]
### Step 5: Combining the Probabilities
The events are sequential and without replacement, so the overall probability is the product of the individual probabilities:
[tex]\[ \text{Overall Probability} = \left( \frac{3}{8} \right) \times \left( \frac{2}{7} \right) \times \left( \frac{1}{3} \right) \][/tex]
### Final Computation
[tex]\[ \text{Overall Probability} = 0.375 \times 0.2857 \times 0.3333 \approx 0.0357 \][/tex]
Hence, the probability that the first two marbles drawn are green and the third marble drawn is yellow is approximately:
[tex]\[ 0.0357 \][/tex]
So there you have it! This is a step-by-step solution showing how to find the probability that the first two marbles drawn are green and the third is yellow, which is approximately [tex]\(0.0357\)[/tex].
### Step 1: Determine the Total Number of Marbles
First, we need to understand the composition of the marbles in the bag:
- Red marbles: 3
- Yellow marbles: 2
- Green marbles: 3
So, the total number of marbles in the bag is:
[tex]\[ 3 + 2 + 3 = 8 \][/tex]
### Step 2: Probability of Drawing the First Green Marble
To find the probability of drawing a green marble first, we look at the number of green marbles and the total marbles:
[tex]\[ \text{Probability of drawing first green marble} = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{3}{8} = 0.375 \][/tex]
### Step 3: Probability of Drawing the Second Green Marble
After drawing one green marble, there are now 2 green marbles left and a total of 7 marbles remaining in the bag.
[tex]\[ \text{Probability of drawing second green marble} = \frac{\text{Remaining green marbles}}{\text{Remaining total marbles}} = \frac{2}{7} \approx 0.2857 \][/tex]
### Step 4: Probability of Drawing a Yellow Marble on the Third Draw
After drawing two green marbles, there are 2 yellow marbles left and a total of 6 marbles remaining in the bag.
[tex]\[ \text{Probability of drawing third yellow marble} = \frac{\text{Remaining yellow marbles}}{\text{Remaining total marbles}} = \frac{2}{6} = \frac{1}{3} \approx 0.3333 \][/tex]
### Step 5: Combining the Probabilities
The events are sequential and without replacement, so the overall probability is the product of the individual probabilities:
[tex]\[ \text{Overall Probability} = \left( \frac{3}{8} \right) \times \left( \frac{2}{7} \right) \times \left( \frac{1}{3} \right) \][/tex]
### Final Computation
[tex]\[ \text{Overall Probability} = 0.375 \times 0.2857 \times 0.3333 \approx 0.0357 \][/tex]
Hence, the probability that the first two marbles drawn are green and the third marble drawn is yellow is approximately:
[tex]\[ 0.0357 \][/tex]
So there you have it! This is a step-by-step solution showing how to find the probability that the first two marbles drawn are green and the third is yellow, which is approximately [tex]\(0.0357\)[/tex].
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.