Mathematics

### Question Description

2. How do you know if the events are independent based on the mathematical equation?

3. List three ways that  help you to determine if two events are independent or dependent?

### 1) Independent Events

When two events are said to be independent of each other, what this means is that the probability that one event occurs in no way affects the probability of the other event occurring. An example of two independent events is as follows; say you rolled a die and flipped a coin. The probability of getting any number face on the die in no way influences the probability of getting a head or a tail on the coin.

 P(A|B) = P(A∩B) / P(B), P(B|A) = P(A∩B) / P(A).

The events A and B are said to be independent provided

 P(A|B) = P(A), or, which is the same P(B|A) = P(B).

Neither the probability of A nor B is affected by the occurrence (or a occurrence) of the other event.

2 ) Two events are said to be independent if the result of the second event is not affected by the result of the first event.

If A and B are independent events, the probability of both events occurring is the product of the probabilities of the individual events

If A and B are independent events,
P(A and B) = P(A) • P(B).

If the result of one event IS affected by the result of another event, the events are said to bedependent.

If A and B are dependent events, the probability of both events occurring is the product of the probability of the first event and the probability of the second event once the first event has occurred.

If A and B are dependent events,
and A occurs first,
P(A and B) = P(A) • P(B,once A has occurred)
... and is written as ...
P(A and B) = P(A) • P(B|A)

University of Virginia
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