Learn about the differences between the two types of events Show
What are Dependent Events vs Independent Events?In mathematics, specifically statistics, events are often classified as dependent or independent. As a basic rule of thumb, the existence or absence of an event can provide clues about other events. Read on to find out more about dependent events vs independent events. In general, an event is deemed dependent if it provides information about another event. An event is deemed independent if it offers no information about other events.  Summary:
What are Dependent Events?For events to be considered dependent, one must have an influence over how probable another is. In other words, a dependent event can only occur if another event occurs first. While this is a mathematic/statistical term, speaking specifically to the subject of probabilities, the same is true of dependent events as they occur in the real world. For example, say you’d like to go on vacation at the end of next month, but that depends on having enough money to cover the trip. You may be counting on a bonus, a commission, or an advance on your paycheck. It also most likely depends on you being given the last week of the month off to make the trip. The primary focus when analyzing dependent events is probability. The occurrence of one event exerts an effect on the probability of another event. Consider the following examples:
What are Independent Events?An event is deemed independent when it isn’t connected to another event, or its probability of happening, or conversely, of not happening. This is true of events in terms of probability, as well as in real life, which, as mentioned above, is true of dependent events as well. For example, the color of your hair has absolutely no effect on where you work. The two events of “having black hair” and “working in Allentown” are completely independent of one another. Independent events don’t influence one another or have any effect on how probable another event is. Other examples of pairs of independent events include:
Additional ResourcesThank you for reading CFI’s guide to Dependent Events vs Independent Events. To keep learning and developing your knowledge of financial analysis, we highly recommend the additional CFI resources below:
What Are Independent and Dependent Events? Probability tells us the likelihood of an event taking place or not. It is represented between numbers 0 and 1, with 1 showing certainty and 0 representing impossibility of occurrence of an event. If the probability is a number closer to 1, it represents a higher likelihood of happening. However, if the number is closer to 0, then the event has fewer chances of taking place. In probability, the event is defined as the outcome of the experiment. These events can be classified as independent events and dependent events. Independent events are those events that occur freely of each other. In other words, the incidence of one event doesn't hinder or affect the occurrence of another event. For example, the outcomes of two rolling dies do not depend on each other. The outcome of one die doesn't affect or change the outcome of the second die. Two events are independent if one or more of the following are true. P(A|B) = P(A), P(B|A) = P(B), P(A ∩ B) = P(A) P(B) Dependent events are those events that rely on each other. In simpler words, the occurrence of one influence the incidence of the other event.We look at the probability of events that have little to no connection to each other. We also look at events that basically caused by each other. These are very common situations to find your self in on a daily basis if you work is related to the finance field. The most common physical objects that are used with this math are marbles, cards, colored balls, and I often see pulling names out of a hat. Get Free Worksheets In Your Inbox!Click the buttons to print each worksheet and answer key.Meet the SkillTwo events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed. Two events, A and B, are independent if the outcome or occurrence of the first event does not affect the probability or outcome of the second event.
Try the SkillYou choose two objects at random, without putting them back in. What is the probability that you get a sphere, a cube in any order?
Practice the Skill TwiceWe have a bag that contains 7 letters A, B, C, D, E, F, G. You choose three objects at random, without putting them back in. What is the probability that you will get these outcomes?
Show the SkillWhat is the probability of drawing an orange ball without putting it back. Then drawing a black ball?
Warm UpThis can make for great class discussions.
Independent Events: IntroductionThree cards are to be drawn from a standard deck of cards. Find the probability of drawing a Jack, then a 10 and a Ace, after replacing the other two.
Independent Events- Worksheet 1In a file, there are 6 Math papers, 5 Geography papers, and 8 English papers. If you select three papers at random, what is the probability of getting English then a Geography paper from the file without replacing first paper?
Worksheet 2In a middle school of 80 students, 42 girls and 38 boys. What is the probability that if two students were randomly chosen, the first is a boy and then a girl sequentially?
Cards At RandomIf there are 21 people sitting in a bus, 7 are children, 11 are women and 3 are men. One person is selected and then replaced. Another person is selected from bus. What is the probability that first person is a woman and the other person is a man?
Independent Events QuizA bottle contains 15 marbles: 5 are grey, 7 are green and 3 are yellow. What is the probability for picking a grey and then a green marble without replacing first?
"Do Now"What is the probability that a randomly selected 10 to 40 number is divisible by 2 and then divisible by 6 after replacing first?
Worksheet 1Jay and Rex are playing tennis. Probability of Jay winning the tennis game is .45 So what is the probability of Rex winning?
Worksheet 2Each of the letters in the word CONNECT are on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be C?
ReviewA jar contains 10 indigo cones, 12 red cones, and 4 grey cones and you pick one without looking. What is the probability that the cone will not be indigo?
QuizThere are 11 marbles in a bag and 4 of them are green. If one marble is chosen, what is the probability that it will be green?
Warm UpA number from 50 to 70 is drawn at random. What is the probability that the number drawn is not divisible by 5?
How do you calculate the probability of dependent events?Dependent events: Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.
What is dependent probability?Two events are dependent if the outcome of the first event affects the outcome of the second event, so that the probability is changed.
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Probability of independent and dependent events answer key
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