4. Multiplication Rule for Independent Events
e. explain the multiplication, addition, and total probability rules;
f. calculate and interpret 1) the joint probability of two events, 2) the probability that at least one of two events will occur, given the probability of each and the joint probability of the two events, and 3) a joint probability of any number of independent events.
g. distinguish between dependent and independent events;
What does it mean for two events to be independent of each other?
Two events, A and B, are independent if and only if
P(A|B) = P(A), or equivalently,
P(B|A) = P(B). That is, the occurrence of one event has no influence on the probability of the occurrence of the other event.
- E.g. if you flip a coin, the result of the first coin has no influence on the outcome of the second flip
What is the multiplication rule for independent events?
If two events are completely independent from each other (i.e., one happening has no bearing on the other's outcome), then:
$$P(A and B) = P(A) * P(B)$$
- E.g. the probability of getting heads on two coin tosses:
1/2 * 1/2 = 1/4 = .25