Question

Match the following events with their corresponding complementary event on rolling a die once.

• A. Odd number
• B. {4, 5, 6}
• C. {1, 4, 5, 6}
• D. {1}

Answer 1

Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complementary events add up to 1 (i.e the outcomes of both the events complete the sample space).

When a die is rolled:
We cannot get an odd and even number at the same time. Hence they are complementary events.
Similarly,
The event of getting {1} and {2, 3, 4, 5, 6} are complementary events.

The event of getting {2, 3} and {1, 4, 5, 6} are complementary events.

The event of getting {1, 2, 3} and {4, 5, 6} are complementary events.