: Probability = chance = odds An event is one or more outcomes of an experiment An outcome is the result of a single trial of an experiment

We have a bag with four balls in it. They are all the same size and shape, so that if you blindly put your hand in the bag, you can not tell which ball you are holding without pulling it out to identify the color.

 What is the probability of drawing twice and choosing a red ball and blue ball?

2 ways the event can occur and 12 possible outcomes

Adding an orange ball to our bag, now what is the probability of drawing twice and choosing a red and blue ball?

We add a purple ball, and want to draw twice and choose a red and blue ball. What is the probability?

Going back to a bag with 5 balls in it, now we draw three times and want to choose a red, blue and green ball. What is the probability?

 This can get very time consuming, very fast. To model just the 5 ball portion of our lottery situation, how many colored balls would we need to have and how many would we have to choose?  Using the data we have figured out so far, can you come up with an algebraic equation to calculate probability? Use the variable n for the number of balls in the experiment and k for the number of balls chosen and P for the probability.

Let’s try our equation….

 Using this information, can you calculate the probability of picking the first 5 numbers correctly?  Remember, there are 59 balls and we are choosing 5 balls.  Now calculate the probability of choosing the powerball using the equation. (You can see it is a 1/39 probability, but check the equation)

 It looks like we have two different probabilities, so how do we combine them to find the overall probability of finding the lottery?  Do we add the two probabilities? Subtract them? Multiply them? Divide? Or something else? Discuss with a partner what you think.

 Remember when we had 4 balls in a bag and needed to choose a red and blue, the probability was 1/6. What if after than we put the four balls back in the bag and chose one ball.

If we were wanting to select a red ball, it would have a probability of 1/4 and 1/4 of 1/6 is 1/24. Look at the circle below and the red represents the event where the choosing two balls out of 4 balls and then choosing 1 ball out of 4.

 Okay, so now what is the probability of someone picking 5 balls out of 59 and also 1 ball out of 39?

 Think of a scenario where you would want to be able to determine the probability of an event. You need to be very specific and give a lot of detail, but don’t calculate the probability…we will do that in a few days!