Question

A class in advanced physics is composed of 10 juniors, 30 seniors, and 10 graduate students. the final grades show that 3 of the juniors, 10 of the seniors, and 5 of the graduate students received an a for the course. if a student is chosen at random from this class and is found to have earned an a, what is the probability that he or she is a senior?

Answer 1

Solution: We are given:

Total students = 10 + 30 + 10 =50

Number of students who received A grade = 3 + 10 + 5 = 18

Number of senior student's who received A grade is = 10

Let A be the event that the student is senior and B be the event that he or she earned an A. Then,

$P(A \cap B)=\frac{10}{50}$

$P(B) = \frac{18}{50}$

Now the probability a student chosen at random from this class and is found to have earned an A, the probability that he or she is a senior is:

$P(A|B) = \frac{P(A \cap B}{P(B)}$

                 $=\frac{\frac{10}{50} }{\frac{18}{50} }$

                 $=\frac{10}{18}=\frac{5}{9} =0.556$