For example, when flipping two coins, there are four possible outcomes: Heads and heads (HH), heads and tails (HT), or tails and tails (TT). If the event is 'at least one tail', then two of the outcomes are included in the event.
A certain event is an event that will always happen. The probability of a certain event is P(e) = 1. An impossible event is an event that will never occur. The probability of an impossible event is P(e) = 0.
In probability, complementary events are two or more events where the outcome must be exactly one of the events. For example, when flipping a coin, the outcome must be either heads or tails. Since you can get either a head or a tail but not both a head and a tail on the same flip, the events are complementary.
When rolling a dice, the events of rolling a 1 and rolling a 2 are not complementary. The events of rolling a 3, 4, 5, or 6 can occur, so rolling a 1 and 2 are not all of the events that can occur. For people, the events of hair color and gender (male or female) are not complementary. Males and females can both have any color hair, so the events male and blonde overlap.
|Experiment||Sample Space||Event||Number of Elements|
|Tossing three coins.||HHH, HHT, HTT, TTT||Exactly two heads||1: HHT|
|Drawing a card from a 52 card deck.||A, 2, 3, 4, 5, 6, 7, 8, 9, J, Q, K||Drawing a king.||4: There are 4 kings in a 52 card deck.|
|Selecting 4 people at random.||F=female, M=male; FFFF, FFFM, FFMM, FMMM, MMMM||Selecting at least three males.||2: FMMM, MMMM.|
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