Independent eventsare a list of events where knowledge of one has no influence on the other. That is easily expressed using conditional probabilities. A and B are independent if:
P (A I B) = P (A), and P(B I A) = P(B)
The best examples of independent events are found with the a priori probabilities of dice throws or coin flips. A die has no memory; therefore, the event of a "4" on a second throw of a die is independent of a "4" on the first throw.
j: Calculate a joint probability of any number of independent events.
The multiplication rule for independent eventsis:
P (A I B) * P(B) = P(A) * P(B) = P(AB)
P (B I A) * P(A) = P(B) * P(A) = P(AB)
Example:On the roll of two dice, the probability of getting two "4s" is:
P(4 on first die and 4 on second die) = P(4 on first die) * P(4 on second die)
P(4 on first die and 4 on second die) = (1/6) *(1/6) = 1/36 = .0278.
k: Calculate, using the total probability rule, an unconditional probability.