Math Problem Statement
A test is given to a group of students; the grades and gender of the students is summarized in the table below:
Cont Table 3.PNG
If one student is chosen at random, determine the following probabilities. Write your answer as fractions.
a) P(student is female) =
b) P(student got an “A”) =
c) P(student is female and got an “A”) =
d) P(student got a "A" given that the student is female) =
e) P(student is female given that the student got an "A") =
Solution
Since I can't see the image you referenced, could you provide me with the data from the table? Once I have that, I can help you with the probability calculations.
For each probability:
- a) is the probability of selecting a female student.
- b) is the probability of selecting a student who got an "A".
- c) is the joint probability of selecting a female student who also got an "A".
- d) is the conditional probability of getting an "A" given the student is female.
- e) is the conditional probability of being female given the student got an "A".
Once I have the data, I can calculate everything.
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Math Problem Analysis
Mathematical Concepts
Probability
Conditional Probability
Basic Fractions
Formulas
P(A) = Number of favorable outcomes / Total outcomes
P(A and B) = P(A) * P(B)
P(A|B) = P(A and B) / P(B)
Theorems
Law of Total Probability
Bayes' Theorem
Suitable Grade Level
Grades 9-12
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