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๐ŸŽฒ Basic Probability & Complementary Events Lab

"At least one" gets
much easier flipped around

Check the basic definition of probability, then find out how a complicated problem like "the probability that at least one is ~" becomes much easier by flipping it into a complementary event (1โˆ’P).

Probability is a number representing how likely something is to happen. It's calculated as the share our desired outcome takes up among every possible outcome, and it always comes out between 0 (will never happen) and 1 (will definitely happen).

A complementary event is the probability that something does not happen. Since the probability of an event and its complement always add up to 1, P(complement)=1โˆ’P(event) holds. A problem like "the probability that at least one is ~" often has too many cases to count directly โ€” but flip it around and find "the probability that none are ~" instead, then subtract from 1, and it becomes much simpler.

Probability shows up constantly in real life too โ€” the chance of rain in a weather forecast, the odds of winning the lottery. Switch between the tabs and work through basic probability, then complementary events, in order.

Probability is "the share of the desired outcome among the total number of possible outcomes." Use the slider to change the number of red balls (a win) and see how the probability changes.
Number of red balls (win)3/ 12
P(win) = number of wins รท total number
A complementary event: P(complement of A) = 1โˆ’P(A). Rolling n dice and directly counting the number of ways to get "at least one 6" is complicated, since there are so many cases. But the opposite, "no 6 at all," is easy to calculate โ€” so subtracting it from 1 gives you the answer right away.
Number of dice n2