17
Mar
Conditional Probability Independent Events. If 3 Statistics books are selected from 6 different Statistics books and 2 Science books are chosen from 5 different Science books how many ways can the five books be arranged on a shelf. Two events A and B are independent if the probability P A B of their intersection A B is equal to the product P A P B of their individual probabilities. This is the same as the o cial de nition. P AB P A or which is the same.
The equation above may be considered as a definition of independent events. Conditional Probabilities and Independent Events Suppose one wants to know the probability that the roll of two dice resulted in a 5 if it is known that neither die showed a 1 or a 6. PrE F PrE PrF. Although typically we expect the conditional probability PAmid B to be different from the probability PA of A it does not have to be different from PA. P BA P B. The events A and B are said to be independent provided.
PrE F PrE PrF.
Events can be Independent meaning each event is not affected by any other events. If the equation is violated the two events. Conditional Probabilities and Independent Events Suppose one wants to know the probability that the roll of two dice resulted in a 5 if it is known that neither die showed a 1 or a 6. Using Addition with Probability Inclusive events are events that can occur at the same time. Let F be got a 3 on second roll. Then the measurement of such a chance is called conditional probability.