Question

P(A) + P(A Ì…) = 1 is one way to express___________.

1) Law of Total Probability
2) Bayes' Theorem
3) Complementary Probability
4) Conditional Probability

Answer 1

The equation P(A) + P(A') = 1 expresses the principle of Complementary Probability, which indicates that the sum of the probabilities of an event and its complement is always one. The correct answer is option 3).

Step-by-step explanation:

The equation P(A) + P(A') = 1 represents the principle of Complementary Probability. This principle states that the probability of an event occurring plus the probability of its complement occurring equals one, as an event either happens or does not happen.

The complement of an event A, denoted A', consists of all the outcomes in the sample space that are not in A. When we say 'the probability of A or A' occurring,' we are taking into account all possible outcomes. An example of complementary probability is considering the flipping of a coin.

Let A be the event where the coin lands on heads. Now, A' would be the event where the coin lands on tails, and since these are the only two possible outcomes, P(A) + P(A') must equal 1. This relationship helps us quickly determine the likelihood of an event not occurring if we know the probability of it occurring.