At a certain college, \(30 \%\) of the students major in engineering, \(20 \%\) play club sports, and \(10 \%\) both major in engineering and play club sports. A student is selected at random.

a. What is the probability that the student is majoring in engineering?

b. What is the probability that the student plays club sports?

c. Given that the student is majoring in engineering, what is the probability that the student plays club sports?

d. Given that the student plays club sports, what is the probability that the student is majoring in engineering?

e. Given that the student is majoring in engineering, what is the probability that the student does not play club sports?

f. Given that the student plays club sports, what is the probability that the student is not majoring in engineering?