The Probability that a student selected at random is taking a statistics class is .12 and the probability that s tudent selected at random is taking an english

Question

The Probability that a student selected at random is taking a statistics class is .12 and the probability that s tudent selected at random is taking an english class is .30. Assuming that the two classes are independent, what is the probability that a student selected at random is taking a statistic class and an english class?

Answer 1

Let us consider events and their probabilities which are provided here.
An event that a student selected at random is taking a statistics class. Let us denote it by A.

Prob(A) = 0.12.
Second event is that a student selected at random is taking an English class. Let us denote it by B.

Prob(B)=0.3.
We are to find the probability that a student selected at random is taking a statistic class and an english class,

which is expressed by formula as Prob(B∩A). 

We know that when events are independent then 

Prob(B∩A) = Prob(A) * Prob(B).

Hence Prob(B∩A) = 0.12 * 0.3 = 0.036.