3.2 Independent and Mutually Exclusive Events & 3.3 Two Basic Rules of Probability

The OR of Two Events

An outcome is in the event A OR B if the outcome is in A, is in B, or is in both A and B.

Sampling with Replacement

If each member of a population is replaced after it is picked, then that member has the possibility of being chosen more than once.

Dependent Events

If two events are NOT independent, then we say that they are dependent.

Multiplication rule

P(A AND B) = P(A|B)P(B)

Addition rule

P(A OR B) = P(A) + P(B) - P(A AND B)

The Conditional Probability of One Event Given Another Event

P(A|B) is the probability that event A will occur given that the event B has already occurred.

Independent events

The occurrence of one event has no effect on the probability of the occurrence of another event. Events A and B are independent if one of the following is true: P(A|B) = P(A) P(B|A) = P(B) P(A AND B) = P(A)P(B)

Mutually exclusive

Two events are mutually exclusive if the probability that they both happen at the same time is zero. If events A and B are mutually exclusive, then P(A AND B) = 0.

Sampling without Replacement

When sampling is done without replacement, each member of a population may be chosen only once.