What is Conditional Probability?

Conditional Probability

The probability of event B occurring that event A has already occurred is read "the probability of B given A" and is written: P(B|A)

What is Dependent Events?

Dependent Events

If the occurrence of one event does affect the probability of the other occurring, then the events are dependent.

What is Specific Multiplication Rule?

Specific Multiplication Rule

Only valid for independent events

P(A and B) = P(A) * P(B)
Example 3:

P(A) = 0.20, P(B) = 0.70, A and B are independent.

The 0.14 is because the probability of A and B is the probability of A times the probability of B or 0.20 * 0.70 = 0.14.

What is Independent Events?

Independent Events

Two events are independent if the occurrence of one does not change the probability of the other occurring.

An example would be rolling a 2 on a die and flipping a head on a coin. Rolling the 2 does not affect the probability of flipping the head.

If events are independent, then the probability of them both occurring is the product of the probabilities of each occurring.

What is Interpreting the table?

Interpreting the table

Certain things can be determined from the joint probability distribution. Mutually exclusive events will have a probability of zero. All inclusive events will have a zero opposite the intersection. All inclusive means that there is nothing outside of those two events: P(A or B) = 1.

What is General Addition Rule?

General Addition Rule

Always valid.

P(A or B) = P(A) + P(B) - P(A and B)
Example 2:

Given P(A) = 0.20, P(B) = 0.70, P(A and B) = 0.15

What is Non-Mutually Exclusive Events?

Non-Mutually Exclusive Events

In events which aren't mutually exclusive, there is some overlap. When P(A) and P(B) are added, the probability of the intersection (and) is added twice. To compensate for that double addition, the intersection needs to be subtracted.