Question

A professor is studying to see if there is a relationship between the grades and gender of his students. He picks a random sample of his students and notes their grades (A, B, or C) and their gender (male or female). He finds that:

1. 28% are A students.
2. 58% are B students.
3. 62% of his students are female.
4. Of those who are female, one-third are A students.
5. Of those who are B students, three-fifths are female students.

What percentage of the students are male and have a C grade?

Answer 1

We know the following probabilities

28% are A students.

A randomly selected student has an A grade is

58% are B students.

A randomly selected student has a B grade is

A randomly selected student has a C grade is (Only A,B, or C grades are given)

62% of his students are female.

A randomly selected student is a female is

A randomly selected student is a male is

Of those who are female, one-third are A students.

Of those who are B students, three-fifths are female students

The probability that a randomly selected student is female and has an A grade is

The probability that a randomly selected student is female and has a B grade is

Using the law of total probabilities we can get the probability that a randomly selected student is female and has a C grade using

Using the law of total probabilities again, we can get the probability that a randomly selected student is male and has a C grade using

ans: The percentage of the students are male and have a C grade is 7.47%