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") =

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.

A test is given to a group of students; the grades and gender of the students is summarized in the table below:

If one student is chosen at random, determine the following probabilities:
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") =

Learn how to calculate probabilities and conditional probabilities using a distribution of student grades and genders. This problem covers key probability concepts, including the law of total probability and Bayes' theorem. Suitable for students in Grades 9-12.

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