Concept about random events

When we are calculating probability, we are concerned with the chance of one particular event from that sample space occurring. Events can be simple or compound. A simple event results in just one outcome. For instance, if we flip one coin, it will result in just one outcome. The coin could either land on heads, or it could land on tails. A compound event is an event containing more than one outcome. For example: rolling a 2 followed by rolling an odd number with a die. Events can sometimes be labeled as complementary events. One event is complementary to another when that event can occur if, and only if, the other does not occur. Again, let’s consider a coin toss with just one coin. The complement of flipping heads would be flipping tails. One can only occur if the other does not occur. Another way of saying this is that events are complementary if their sample space includes all possible outcomes, meaning that the sum of their probabilities is 1. Compatible events are events that can occur at the same time. Incompatible events cannot occur at the same time. If events A and B are incompatible, it is impossible for both A and B to happen at the same time. For instance, if you are rolling a typical die and event A is to roll a 1, 2, or 3 and event B is to roll a 4, 5, or 6, then events A and B are incompatible. It is not possible for both A and B to occur at the same time. If, however, event A is to roll an even number and event B is to roll a number larger than 3, then events A and B are compatible, because it is possible for both events to occur at the same time. Finally, probability events can be grouped as either dependent or independent. With dependent events, the probability of the second outcome can change based on the results of the first. Two events are said to be independent when the outcome of one event does not change the probability of the other. If you are drawing two cards from a regular deck of playing cards, drawing one card out at a time and replacing that card back into the deck each time, then the outcome of the first draw would not affect the outcome of the second. These would be independent events. If, however, you were not replacing the card that you drew out on the first draw, then the probability of the second draw would be affected by the first event. There would be fewer cards remaining for the second draw, and the card that you drew on your first turn would not be available the second time. These would then be dependent events. Denise is conducting a probability experiment, using the two spinners shown here. She is going to spin both spinners at the same time and wants to determine the probability of the first spinner landing on white (Event A) and the probability of the second spinner landing on grey (Event B).

Four Basic Types of Events

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