Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Let's analyze each of the provided statements using probabilities derived from the given table:
### Table Overview
The given table shows the distribution of flowers by color and type:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Type of Flower/Color} & \text{Red} & \text{Pink} & \text{Yellow} & \text{Total} \\ \hline \text{Rose} & 40 & 20 & 45 & 105 \\ \hline \text{Hibiscus} & 80 & 40 & 90 & 210 \\ \hline \text{Total} & 120 & 60 & 135 & 315 \\ \hline \end{array} \][/tex]
### Probabilities
- Total number of flowers: 315
- Total number of yellow flowers: 135
- Total number of roses: 105
- Total number of hibiscus: 210
- Total number of red flowers: 120
- Total number of pink flowers: 60
#### Calculation of Probabilities:
1. [tex]\( P(\text{flower is yellow}) \)[/tex]
[tex]\[ P(\text{flower is yellow}) = \frac{135}{315} \approx 0.42857142857142855 \][/tex]
2. [tex]\( P(\text{flower is a rose}) \)[/tex]
[tex]\[ P(\text{flower is a rose}) = \frac{105}{315} \approx 0.3333333333333333 \][/tex]
3. [tex]\( P(\text{flower is a hibiscus}) \)[/tex]
[tex]\[ P(\text{flower is a hibiscus}) = \frac{210}{315} \approx 0.6666666666666666 \][/tex]
4. [tex]\( P(\text{flower is red}) \)[/tex]
[tex]\[ P(\text{flower is red}) = \frac{120}{315} \approx 0.38095238095238093 \][/tex]
### Statements Assessment:
A. [tex]\( P(\text{flower is yellow | flower is a rose}) \neq P(\text{flower is yellow}) \)[/tex]
[tex]\[ P(\text{flower is yellow | flower is a rose}) = \frac{45}{105} \approx 0.42857142857142855 \][/tex]
Compare:
[tex]\[ P(\text{flower is yellow}) \approx 0.42857142857142855 \][/tex]
Both probabilities are equal, so this statement is false.
B. [tex]\( P(\text{flower is a hibiscus | color is red}) = P(\text{flower is a hibiscus}) \)[/tex]
[tex]\[ P(\text{flower is a hibiscus | color is red}) = \frac{80}{120} \approx 0.6666666666666666 \][/tex]
Compare:
[tex]\[ P(\text{flower is a hibiscus}) \approx 0.6666666666666666 \][/tex]
Both probabilities are equal, so this statement is true.
C. [tex]\( P(\text{flower is a rose | color is red}) = P(\text{flower is red}) \)[/tex]
[tex]\[ P(\text{flower is a rose | color is red}) = \frac{40}{120} \approx 0.3333333333333333 \][/tex]
Compare:
[tex]\[ P(\text{flower is red}) \approx 0.38095238095238093 \][/tex]
Probabilities are not equal, so this statement is false.
D. [tex]\( P(\text{flower is a hibiscus | color is pink}) \neq P(\text{flower is a hibiscus}) \)[/tex]
[tex]\[ P(\text{flower is a hibiscus | color is pink}) = \frac{40}{60} \approx 0.6666666666666666 \][/tex]
Compare:
[tex]\[ P(\text{flower is a hibiscus}) \approx 0.6666666666666666 \][/tex]
Both probabilities are equal, so this statement is false.
### Conclusion
The correct statement is B. [tex]\( P(\text{flower is a hibiscus | color is red}) = P(\text{flower is a hibiscus}) \)[/tex].
### Table Overview
The given table shows the distribution of flowers by color and type:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Type of Flower/Color} & \text{Red} & \text{Pink} & \text{Yellow} & \text{Total} \\ \hline \text{Rose} & 40 & 20 & 45 & 105 \\ \hline \text{Hibiscus} & 80 & 40 & 90 & 210 \\ \hline \text{Total} & 120 & 60 & 135 & 315 \\ \hline \end{array} \][/tex]
### Probabilities
- Total number of flowers: 315
- Total number of yellow flowers: 135
- Total number of roses: 105
- Total number of hibiscus: 210
- Total number of red flowers: 120
- Total number of pink flowers: 60
#### Calculation of Probabilities:
1. [tex]\( P(\text{flower is yellow}) \)[/tex]
[tex]\[ P(\text{flower is yellow}) = \frac{135}{315} \approx 0.42857142857142855 \][/tex]
2. [tex]\( P(\text{flower is a rose}) \)[/tex]
[tex]\[ P(\text{flower is a rose}) = \frac{105}{315} \approx 0.3333333333333333 \][/tex]
3. [tex]\( P(\text{flower is a hibiscus}) \)[/tex]
[tex]\[ P(\text{flower is a hibiscus}) = \frac{210}{315} \approx 0.6666666666666666 \][/tex]
4. [tex]\( P(\text{flower is red}) \)[/tex]
[tex]\[ P(\text{flower is red}) = \frac{120}{315} \approx 0.38095238095238093 \][/tex]
### Statements Assessment:
A. [tex]\( P(\text{flower is yellow | flower is a rose}) \neq P(\text{flower is yellow}) \)[/tex]
[tex]\[ P(\text{flower is yellow | flower is a rose}) = \frac{45}{105} \approx 0.42857142857142855 \][/tex]
Compare:
[tex]\[ P(\text{flower is yellow}) \approx 0.42857142857142855 \][/tex]
Both probabilities are equal, so this statement is false.
B. [tex]\( P(\text{flower is a hibiscus | color is red}) = P(\text{flower is a hibiscus}) \)[/tex]
[tex]\[ P(\text{flower is a hibiscus | color is red}) = \frac{80}{120} \approx 0.6666666666666666 \][/tex]
Compare:
[tex]\[ P(\text{flower is a hibiscus}) \approx 0.6666666666666666 \][/tex]
Both probabilities are equal, so this statement is true.
C. [tex]\( P(\text{flower is a rose | color is red}) = P(\text{flower is red}) \)[/tex]
[tex]\[ P(\text{flower is a rose | color is red}) = \frac{40}{120} \approx 0.3333333333333333 \][/tex]
Compare:
[tex]\[ P(\text{flower is red}) \approx 0.38095238095238093 \][/tex]
Probabilities are not equal, so this statement is false.
D. [tex]\( P(\text{flower is a hibiscus | color is pink}) \neq P(\text{flower is a hibiscus}) \)[/tex]
[tex]\[ P(\text{flower is a hibiscus | color is pink}) = \frac{40}{60} \approx 0.6666666666666666 \][/tex]
Compare:
[tex]\[ P(\text{flower is a hibiscus}) \approx 0.6666666666666666 \][/tex]
Both probabilities are equal, so this statement is false.
### Conclusion
The correct statement is B. [tex]\( P(\text{flower is a hibiscus | color is red}) = P(\text{flower is a hibiscus}) \)[/tex].
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
