Disjoint vs complementary events

Disjoint events are events that cannot happen at the same time, while complementary events are events that cannot happen at the same time and whose probabilities add up to 1.

Here are some simple examples to help a child understand the difference between disjoint and complementary events:

Disjoint events:

Flipping a coin and getting heads or getting tails. These events cannot happen at the same time, so they are disjoint.

Drawing a red ball or a blue ball from a bag of balls. These events cannot happen at the same time, so they are disjoint.

Complementary events:

Flipping a coin and getting heads or getting tails. These events cannot happen at the same time, and the probability of getting heads is 50% and the probability of getting tails is 50%, so these events are complementary.

Drawing a red card or a black card from a deck of cards. These events cannot happen at the same time, and the probability of drawing a red card is 26/52 and the probability of drawing a black card is 26/52, so these events are complementary.