Independent vs Dependent Events Intro to AlgebraGeometry Events

Independent vs Dependent Events Intro to Algebra/Geometry

Events Sometimes we are asked the probability of multiple things happen. When this occurs we have to determine if the first event has any effect on the probability of the second event occuring.

Independent Events can be "Independent", meaning each event is not affected by any other events.

Independent Events This is an important idea! A coin does not "know" that it came up heads before. . . each toss of a coin is a perfect isolated thing. Some people think "it is overdue for a Tail", but really truly the next toss of the coin is totally independent of any previous tosses.

Dependent Event But some events can be "dependent". . . which means they can be affected by previous events.

So what makes an event dependent?

Dependent Events After taking one card from the deck and not replacing that card, then there are less cards available, so the probabilities changes for the next draw!

Independent vs Dependent • Replacement: When you put each card back after drawing it the chances don't change, as the events are independent. • Without Replacement: The chances will change, and the events are dependent.

Finding the Probability of Independent Events What is the probability of tossing a coin in the air and getting a head, and tossing again and getting another head?

Independent Events 1. Find the probability of each event seperately 2. Multiply the probabilities

Finding the Probability of Dependent Events What is the probability of drawing a club from a deck of cards, and then drawing a heart without replacement?

Dependent Events 1. Find the probability of the first event 2. Find the probability of the second event assuming that the first event happened. 3. Multiply the probabilities.