Explanation

The problem indicates that the events occur independently of each other. Therefore, in calculating Quantity A, do not just add both events, even though it is an “or” situation. Adding 0.3 + 0.2 = 0.5 is incorrect because the probability that both events occur is counted twice. (Only add probabilities in an “or” situation when the probabilities are mutually exclusive.)

While Quantity A’s value should include the probability that both events occur, make sure to count this probability only once, not twice. Since the probability that both events occur is 0.3(0.2) = 0.06, subtract this value from the “or” probability.

Quantity A: Add the two probabilities (rain or pop quiz) and subtract both scenarios (rain and pop quiz): 0.3 + 0.2 – (0.3)(0.2) = 0.44
Quantity B: Multiply the probability that rain does not occur (0.7) and the probability that the pop quiz does not occur (0.8): 0.7(0.8) = 0.56

Alternatively, note that the two quantities, collectively, include every possibility and are mutually exclusive of one another (Quantity A includes “rain and no quiz,” “quiz and no rain,” and “both rain and quiz,” and Quantity B includes “no rain and no quiz”). Therefore, the values of Quantities A and B must sum to 1. Calculating the value of either Quantity A or Quantity B would automatically indicate the value for the other quantity.

If you do this, calculate Quantity B first (because it’s the easier of the two quantities to calculate) and then subtract Quantity B from 1 in order to get Quantity A’s value. That is, 1 – 0.56 = 0.44.