Mutually exclusive events refer to a combination of outcomes that cannot occur at the same time. For instance, one either has to engage the reverse or forward gear in a vehicle, but cannot engage both gears at the same time. Engaging the reverse gear and engaging the forward gear are mutually exclusive events. Events are termed to as independent events if the occurrence of one of the events does not affect the occurrence and outcome of the other event. An example of independent events is picking two numbers from two jars, one from each jar, with the numbers randomly folded up. When one chooses two as the first number, this does not affect the likelihood of picking a two or any other figure from the second jar.
There is a relationship between independent events and mutually exclusive events as most mutually exclusive events cannot be termed as independent events, but are instead dependent events. The example of either engaging the reverse or forward gear is an example of events that are mutually exclusive but dependent. The outcome of engaging the reverse gear is dependent on whether or not one has engaged the forward gear. If one has engaged the forward gear, then the occurrence of engaging the reverse gear is hindered, and thus events are dependent events. On the other hand, independent events cannot be termed as solely mutually exclusive as they could be either mutually exclusive or not. There are some events that are dependent but not mutually exclusive. An example is skiing when it’s snowing. Skiing is dependent on the presence of snow, thus making it a dependent event. At the same time, the events are not mutually exclusive as both skiing and snowing take place at the same time.