Suppose that we have 6 blue balls and 4 yellows placed in two boxes as seen below. I ask you to randomly pick a ball. The probability of getting a blue ball is 6 / 10 = 0,6. What if I ask you to pick a ball from box A? The probability of picking a blue ball clearly decreases. The condition here is to pick from box A which clearly changes the probability of the event (picking a blue ball). The probability of event A given that event B has occurred is denoted as p(A|B).
Here, P(B) = Probability of a car buyer chosen at random bought an alarm system, which is 40/100 = 0.4 P(A,B) = Probability of both happening together, which is given 20/100 = 0.2 So, P(A|B) = 0.2/0.4 = 0.5