Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Sure, let's go through each part step by step based on the given data in the table.
1. Probability that the student got an [tex]$A$[/tex]:
To find this probability, we simply divide the number of students who got an A by the total number of students.
[tex]\[ \text{P(A)} = \frac{\text{Number of students who got an A}}{\text{Total number of students}} = \frac{15}{48} = 0.3125 \][/tex]
2. Probability that the student was female AND got an [tex]$A$[/tex]:
To find this probability, we need the number of females who got an A divided by the total number of students.
[tex]\[ \text{P(Female and A)} = \frac{\text{Number of females who got an A}}{\text{Total number of students}} = \frac{4}{48} = 0.0833 \][/tex]
3. Probability that the student was female OR got a [tex]$C$[/tex]:
To find this probability, we use the formula for the probability of the union of two events:
[tex]\[ \text{P(Female or C)} = \text{P(Female)} + \text{P(C)} - \text{P(Female and C)} \][/tex]
Where:
- [tex]\( \text{P(Female)} \)[/tex] is the probability of a student being female;
- [tex]\( \text{P(C)} \)[/tex] is the probability of a student getting a C;
- [tex]\( \text{P(Female and C)} \)[/tex] is the probability of a student being female and getting a C.
Calculating these individually:
[tex]\[ \text{P(Female)} = \frac{\text{Total number of females}}{\text{Total number of students}} = \frac{18}{48} \][/tex]
[tex]\[ \text{P(C)} = \frac{\text{Number of students who got a C}}{\text{Total number of students}} = \frac{11}{48} \][/tex]
[tex]\[ \text{P(Female and C)} = \frac{\text{Number of females who got a C}}{\text{Total number of students}} = \frac{5}{48} \][/tex]
Combining these:
[tex]\[ \text{P(Female or C)} = \left( \frac{18}{48} + \frac{11}{48} - \frac{5}{48} \right) = \frac{24}{48} = 0.5 \][/tex]
4. Probability that the student was female GIVEN they got a B:
To find this conditional probability, we divide the number of females who got a B by the total number of students who got a B:
[tex]\[ \text{P(Female | B)} = \frac{\text{Number of females who got a B}}{\text{Total number of students who got a B}} = \frac{9}{22} = 0.4091 \][/tex]
So the final probabilities are:
1. Probability that the student got an [tex]$A$[/tex]: [tex]\( \boxed{0.3125} \)[/tex]
2. Probability that the student was female AND got an [tex]$A$[/tex]: [tex]\( \boxed{0.0833} \)[/tex]
3. Probability that the student was female OR got a [tex]$C$[/tex]: [tex]\( \boxed{0.5} \)[/tex]
4. Probability that the student was female GIVEN they got a B: [tex]\( \boxed{0.4091} \)[/tex]
1. Probability that the student got an [tex]$A$[/tex]:
To find this probability, we simply divide the number of students who got an A by the total number of students.
[tex]\[ \text{P(A)} = \frac{\text{Number of students who got an A}}{\text{Total number of students}} = \frac{15}{48} = 0.3125 \][/tex]
2. Probability that the student was female AND got an [tex]$A$[/tex]:
To find this probability, we need the number of females who got an A divided by the total number of students.
[tex]\[ \text{P(Female and A)} = \frac{\text{Number of females who got an A}}{\text{Total number of students}} = \frac{4}{48} = 0.0833 \][/tex]
3. Probability that the student was female OR got a [tex]$C$[/tex]:
To find this probability, we use the formula for the probability of the union of two events:
[tex]\[ \text{P(Female or C)} = \text{P(Female)} + \text{P(C)} - \text{P(Female and C)} \][/tex]
Where:
- [tex]\( \text{P(Female)} \)[/tex] is the probability of a student being female;
- [tex]\( \text{P(C)} \)[/tex] is the probability of a student getting a C;
- [tex]\( \text{P(Female and C)} \)[/tex] is the probability of a student being female and getting a C.
Calculating these individually:
[tex]\[ \text{P(Female)} = \frac{\text{Total number of females}}{\text{Total number of students}} = \frac{18}{48} \][/tex]
[tex]\[ \text{P(C)} = \frac{\text{Number of students who got a C}}{\text{Total number of students}} = \frac{11}{48} \][/tex]
[tex]\[ \text{P(Female and C)} = \frac{\text{Number of females who got a C}}{\text{Total number of students}} = \frac{5}{48} \][/tex]
Combining these:
[tex]\[ \text{P(Female or C)} = \left( \frac{18}{48} + \frac{11}{48} - \frac{5}{48} \right) = \frac{24}{48} = 0.5 \][/tex]
4. Probability that the student was female GIVEN they got a B:
To find this conditional probability, we divide the number of females who got a B by the total number of students who got a B:
[tex]\[ \text{P(Female | B)} = \frac{\text{Number of females who got a B}}{\text{Total number of students who got a B}} = \frac{9}{22} = 0.4091 \][/tex]
So the final probabilities are:
1. Probability that the student got an [tex]$A$[/tex]: [tex]\( \boxed{0.3125} \)[/tex]
2. Probability that the student was female AND got an [tex]$A$[/tex]: [tex]\( \boxed{0.0833} \)[/tex]
3. Probability that the student was female OR got a [tex]$C$[/tex]: [tex]\( \boxed{0.5} \)[/tex]
4. Probability that the student was female GIVEN they got a B: [tex]\( \boxed{0.4091} \)[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
