Question

1. consider the events from activity 1.1, questions 5 and 6—“rolling an even number” and “rolling a number that is not even.” what do you notice about the sum of the probabilities of these two complementary events?

Explanation:

Complementary events are two outcomes that are the only possible results (they cover all cases with no overlap). For a standard die, even numbers are 2,4,6 (3 outcomes) and non-even (odd) numbers are 1,3,5 (3 outcomes). The probability of rolling an even number is $\frac{3}{6} = \frac{1}{2}$, and the probability of rolling a non-even number is $\frac{3}{6} = \frac{1}{2}$. Their sum is $\frac{1}{2} + \frac{1}{2} = 1$, which is a general rule for all complementary events.

Answer:

The sum of the probabilities of two complementary events equals 1 (or 100%).