These problems make the jump from combinations to probability. The idea is that you have already done some of the basic problems in probability, and the combination problems. The first problem is just warm-up.
It's gym day. Rebecca has two different pairs of sweat pants she could wear. One is black and one is white. She also has 3 different t-shirts she could wear. One is blue, one is brown, and one is red. How many different outfits can she wear?
Explain how you got your answer.
Probability of Combinations
Suppose Rebecca just reaches in her drawer and selects sweat pants and a t-shirt by random. (Remember how I pulled little pom-poms out of my pocket.) So any combination is as likely as any other.
What is the probability that she will wear the black sweat pants?
What is the probability that she will wear the blue t-shirt?
What is the probability that she will wear the black sweat pants and the blue t-shirt?
Suppose Rebecca writes down seperate pieces of paper all of the different combinations of outfits she could wear. (You already calculated how many pieces of paper she would need for each combination, right?) Then she puts the pieces of paper in her pocket, shuffles them around, and picks out one at random. So each outfit is as likely to be selected as each other outfit.
What is the probability that she will choose a paper with black sweat pants?
What is the probability that she will choose a paper with blue t-shirt?
What is the probability that she will pick a paper with black sweat pants and blue t-shirt?
George rolls a die and flips a coin.
How many different outcomes are there? For example, he might roll a 3 and flip heads. That's one outcome.
Are all the outcomes equally likely? Do they all have the same probability?
What is the probability that he will roll a 3 and flip heads?
George flips two coins, a penny and a nickel.
What is the probability that they both come up heads?
What are the possible outcomes?
George flips two coins, both pennies.
What is the probability that they both come up heads?
What are the possible outcomes?
