Dependent or Independent?
Being able to tell the difference between a dependent and independent event is vitally important in solving probability questions. Why? Imagine a single event: winning the lotto. That depends upon you buying a ticket. So winning the lotto and buying a ticket are dependent events. Your odds of winning the lotto if you buy a ticket might be 1/1 million. But what about something unrelated, like driving to work and winning the lotto? Your odds of winning the lotto if you drive your car (and don’t buy a ticket) are zero. So the odds change a lot with different event types.
Dependent or Independent? Steps
Step 1: Ask yourself, is it possible for the events to occurhappen in any order? If no (the steps must be performed in a certain order), go to Step 3a. If yes (the steps can be performed in any order), go to Step 2. If you are unsure, go to Step 2.
Some examples of events that can clearly be performed in any order are:
- Tossing a coin, then rolling a die.
- Purchasing a car, then purchasing a coat.
- Drawing cards from a deck.
Some events that must be performed in a certain order are:
- Parking and getting a parking ticket (you can’t get a parking ticket without parking).
- Surveying a group of people, and finding out how many women are against gun rights (because you are splitting the survey into subgroups, and you can’t split a survey into subgroups without first performing the survey!).
Step 2: Ask yourself, does one event in any way affect the outcome (or the odds) of the other event? If yes, go to step 3a, if no, go to Step 3b.
Some examples of events that affect the odds or probability of the next event include:
- Choosing a card, not replacing it, then choosing another (because the odds of choosing the first card are 1/52, but if you do not replace it, your are changing the odds to 1/51 for the next draw).
- Choosing anything and not replacing it, then choosing another (i.e. choosing bingo balls, raffle tickets).
Some examples of events that do not affect the odds or probability of the next event occurring are:
- Choosing a card and replacing it, then choosing another card (because the odds of choosing the first card are 1/52, and the odds of choosing the second card are 1/52).
- Choosing anything, as long as you put the items back.
Step 3a: You’re done–the event is dependent.
Step 3b:You’re done–the event is independent.
That’s how to find out if an event is Dependent or Independent!