1 and 0
Any probability P(A) is a number between 0 and 1.
Therefore, 0 £ P(A) £ 1.
2: The sample space, S, of all possible outcomes has a probability of 1. Therefore,
P(S) = 1. In other words, the sum of probabilities of all possible outcomes of an event is equal to 1.
P(H) = 0.5
If we believe the coin is unbalanced, we might assign something like:
P(H) = 0.4
The sum of the probabilities getting heads or tails, however, is equal to 1. The probability of getting a head in a coin toss is not necessarily 1/2. Some coins are unbalanced! If an event is certain to occur, its probability is 1. If it is certain not to occur, its probability is 0. For example, the probability of drawing a King of spades from a 52 card deck is 1/52. Since a Red King of spades does not exist, the probability of drawing a Red King of spades is 0.
When there are more than two possible outcomes, the sum of the probabilities is still equal to 1.
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) = 1