Answer to Question #334404 in Statistics and Probability for iqra

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

Answer 1

What is the probability that he or she is a senior?

$P(S|A)=\dfrac{P(S\cap A)}{P(A)}$

$P(S\cap A)=\dfrac{10}{10+30+10}=\dfrac{1}{5}$

$P( A)=\dfrac{3+10+5}{10+30+10}=\dfrac{9}{25}$

$P(S|A)=\dfrac{1/5}{9/25}=\dfrac{5}{9}$