In this lesson, we will determine the probability of two events that are independent of one another. Let's first discuss what the term independent means in terms of probability.
Let's take a look at an example.
Example 1 is pretty easy to comprehend because we are finding the probability of two different events using two different tools. Let's see what happens when we use one tool, like a jar of marbles.
A jar of marbles contains 4 blue marbles, 5 red marbles, 1 green marble, and 2 black marbles.
A marble is chosen at random from the jar. After replacing it, a second marble is chosen.
Find the probability for the following:
P(green and red)
P(blue and black)
This method for calculating the probability of independent events also works if you have more than 2 events occuring sequentially. Check out the practice problem below.
Ok, now it's your turn to practice a probability problem that involves independent events. Just remember to find the probability of each independent event first, then multiply the results together.
You are given a standard deck of 52 cards. Three cards are chosen at random with replacement. What is the probability of choosing an ace, a spade, and a four?
So, how did you do? Independent Events isn't too bad - now we'll take a look at dependent events.