Statistics and Probability-Part 3

Computing Chances Probability is the likelihood of an event occurring. If you want to count the possible ways that something can occur, you can use several strategies: -Drawing Combinations -Making a List -Using a Tree Diagram -Creating a Table -Use calculations. If you know all of the possible outcomes, and you know they have the same chance of occurring, you can make statements about the chance that certain outcomes may occur. You can do this by counting how many times this outcome occurs compared to all possible outcomes. The chance is: Number of favorable outcomes/Total number of possible outcomes

You can express chance as a ratio (fraction), percent, or decimal You can express chance as a ratio (fraction), percent, or decimal. When written as a decimal, events have a chance of occurring between 0 and 1. A probability of 0 indicates the event is highly unlikelyto occur. A probability of 1 indicates that the event is almost certain to occur.

A Class Trip The 7th grade class is planning a two-day trip to a lake for a Science field trip. They can choose to go to one of four lakes: Lake Norma, Lake Ancona, Lake Popo, or Lake Windus. Besides choosing the lake, the class has to choose whether to camp out in a tent or stay in a lodge, and whether to take a bus tour around the lake or a boat trip. The class has to make a lot of decisions! A tree diagram is one way to organize all of the possible outcomes for this trip.

Fill in the tree diagram below, by filling in the correct words on the branches of the trees.

How many different class trips are possible for the class to choose How many different class trips are possible for the class to choose? How many possibilities are there if Robert’s class does NOT want to go camping? Robert’s class finds it hard to decide which trip to choose. Different students like different options. Fiona suggests that they should just write each possible trip on a piece of paper, puts the pieces in a bag, and pick one of the possible trips from the bag. If Robert’s class picks one of the trips from the bag, what is the chance they will go camping? What is the chance they will go to Lake Norma?

Families Nearly as many baby girls as baby boys are born. The difference is so small you can say that the chance of having a boy is equal to the chance of having a girl. Sonya, Matthew, and Sarah are the children of the Jansen family. A new family is moving into the house next to the Jansen house. They already know that this family has three children about the same ages as Sonya, Matthew, and Sarah. “I hope they have two girls and one boy just like we have,” Sonya says, “but I guess there is not much chance that will happen.” Do you think the chance that a family with three children where two are girls and one is a boy will move in next door is more or less than 50%? Explain your reasoning.

The tree diagram shows different possibilities for a family with two children. How many possibilities are there for a family with two children? Explain the difference between paths BG and GB. What is the chance that a family with two children will have two girls?

What is the probability that the family will NOT have two girls What is the probability that the family will NOT have two girls? How did you find this chance? Extend the tree diagram for a family with three children. What is the chance that a family with three children will have two girls and one boy? What is the chance that a family with three children will have two girls and one boy? Write as a fraction, decimal, and percent. What is the chance that a family with three children will have three boys?

About 500 families with three children live in East Lynn About 500 families with three children live in East Lynn. Would you be surprised if 70 of these 500 families with three children had three boys? Explain

Number Cubes You can also count outcomes by using a chart. If you want to see all the possibilities when rolling two dice, you can use this table. Brenda thinks that the chance of rolling a sum of eight with two number cubes is the same as the chance of rolling a sum of 3. Is she correct? What is the probability of rolling two 1’s? What is the probability of rolling one 1?

Codes You need a code to open some school lockers as well as to access ATM machines and often to open garage doors. A four digit code is used for the garage door at Mr. Moore’s home. The code is made up of four numbers from zero to nine. All numbers can be used for more than once. If the code is incorrectly entered three times, the garage is locked for 30 minutes. Mr. Moore’s sister is at the garage door, but she forgot the code. She remembers that the code starts with 3-5 and she knows there are no zeroes in the code. So, the code is 3-5-___-___. She decides to guess. What is the chance her first guess is correct? Suppose she guesses incorrectly. What is the probability that she will be locked outside for the next half hour?