Question
Trisha has 2 boxes of marbles. She selects a marble from each box 100 times, replacing the marble back into its box each time.
From the first box, she selects:
• A white marble 29 times
• A red marble 25 times
• A blue marble 46 times.
From the second box, she selects:
• A yellow marble 27 times
• A green marble 21 times
• An orange marble 52 times.
Based on this information, what is the probability that Trisha will select a red marble from the first box and an orange marble from the second box on her next turn?
From the first box, she selects:
• A white marble 29 times
• A red marble 25 times
• A blue marble 46 times.
From the second box, she selects:
• A yellow marble 27 times
• A green marble 21 times
• An orange marble 52 times.
Based on this information, what is the probability that Trisha will select a red marble from the first box and an orange marble from the second box on her next turn?
Answers
GPT-4o mini
To find the probability that Trisha will select a red marble from the first box and an orange marble from the second box on her next turn, we first need to calculate the probabilities of drawing each marble from their respective boxes.
### Step 1: Calculate the probability of selecting a red marble from the first box.
From the first box, Trisha has selected:
- White marbles: 29 times
- Red marbles: 25 times
- Blue marbles: 46 times
The total number of selections from the first box is:
\[
29 + 25 + 46 = 100
\]
The probability of selecting a red marble from the first box is:
\[
P(\text{Red from Box 1}) = \frac{\text{Number of Red Marbles}}{\text{Total Selections from Box 1}} = \frac{25}{100} = 0.25
\]
### Step 2: Calculate the probability of selecting an orange marble from the second box.
From the second box, Trisha has selected:
- Yellow marbles: 27 times
- Green marbles: 21 times
- Orange marbles: 52 times
The total number of selections from the second box is:
\[
27 + 21 + 52 = 100
\]
The probability of selecting an orange marble from the second box is:
\[
P(\text{Orange from Box 2}) = \frac{\text{Number of Orange Marbles}}{\text{Total Selections from Box 2}} = \frac{52}{100} = 0.52
\]
### Step 3: Calculate the combined probability.
Since the selection of marbles from the two boxes is independent, we can find the combined probability by multiplying the individual probabilities:
\[
P(\text{Red from Box 1 and Orange from Box 2}) = P(\text{Red from Box 1}) \times P(\text{Orange from Box 2}) = 0.25 \times 0.52
\]
Now calculate:
\[
0.25 \times 0.52 = 0.13
\]
### Conclusion
Therefore, the probability that Trisha will select a red marble from the first box and an orange marble from the second box on her next turn is:
\[
\boxed{0.13}
\]
### Step 1: Calculate the probability of selecting a red marble from the first box.
From the first box, Trisha has selected:
- White marbles: 29 times
- Red marbles: 25 times
- Blue marbles: 46 times
The total number of selections from the first box is:
\[
29 + 25 + 46 = 100
\]
The probability of selecting a red marble from the first box is:
\[
P(\text{Red from Box 1}) = \frac{\text{Number of Red Marbles}}{\text{Total Selections from Box 1}} = \frac{25}{100} = 0.25
\]
### Step 2: Calculate the probability of selecting an orange marble from the second box.
From the second box, Trisha has selected:
- Yellow marbles: 27 times
- Green marbles: 21 times
- Orange marbles: 52 times
The total number of selections from the second box is:
\[
27 + 21 + 52 = 100
\]
The probability of selecting an orange marble from the second box is:
\[
P(\text{Orange from Box 2}) = \frac{\text{Number of Orange Marbles}}{\text{Total Selections from Box 2}} = \frac{52}{100} = 0.52
\]
### Step 3: Calculate the combined probability.
Since the selection of marbles from the two boxes is independent, we can find the combined probability by multiplying the individual probabilities:
\[
P(\text{Red from Box 1 and Orange from Box 2}) = P(\text{Red from Box 1}) \times P(\text{Orange from Box 2}) = 0.25 \times 0.52
\]
Now calculate:
\[
0.25 \times 0.52 = 0.13
\]
### Conclusion
Therefore, the probability that Trisha will select a red marble from the first box and an orange marble from the second box on her next turn is:
\[
\boxed{0.13}
\]