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You know that the probability that an event, E, occurs, is P(E). This value is equal to the number of outcomes you are interested in, N(E), divided by the total number of outcomes in the sample space, N(S).
Probability of an Event
P(Event) =\( \frac{N(E)}{N(S)} \)
Whether or not it rains today, the kind of shoes you choose to wear, and the time you eat dinner are all events.
Some events occur by themselves while other events take place together. When two events occur together and one event does not affect the outcome of the other, those events are said to be independent events. If one event affects the outcome of another, then those events are dependent events.
In the video below, an instructor will demonstrate differences between dependent and independent events.
You may want to use the study guide to follow along. If so, click the button below to download the study guide.
Hello! In this video, I would like to share with you methods of calculating probability of both independent and dependent events. To find the probability of two events occurring together you have to decide whether one event occurring affects the likelihood of the other event occurring.
When one event affects how a second can occur, the events are known as dependent events, otherwise they are known as independent events
Consider the following pairs of events. Can you tell which of these are dependent and which of these are independent events? In the first case, picking a card from a deck of cards and rolling a single die do not affect one another. The result from picking the card will not influence how the die will be rolled, so we call these independent events. What if you pick a card at random from a deck, replace it, then pick another? Since the first card was placed back into the deck before the second was chosen, it did not influence the second pick – the exact same set of cards were available for the second choice. Therefore this is a pair of independent events. Had the first card not been replaced, then the pair would be considered dependent since the makeup of the deck for the second choice was different than the first. Not replacing the card would be the same as choosing, two cards from the deck. Finally, what if you roll two separate dice? These are also independent, since the outcome of the first die doesn’t affect the second.
Give It a Shot!
Can you use what you learned in the video to distinguish between dependent and independent events? Use the activity below to find out. Read each flash card and decide if the events are independent or dependent. Click each card to check your answer before moving on.
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