Data Analysis And Probability Ogt

1. Leroy has a number cube with sides labeled 1 through 6. He tosses the number cube 4 times. Each toss results in a 5. What is the likelihood that the next toss will result in a 5?

Students need to make predictions that are based on theoretical or experimental results. For example, the spinner shown has 8 equal sections. The likelihood of the spinner landing on the number 6 is because 4 of the 8 sections are labeled with a 6, or of the circle is marked with 6. Spinning the spinner is an independent event. This means that the outcome of one spin does not affect the outcome of any other spin. For example, suppose that the spinner is spun 3 times and lands on 6 each time. The next time the spinner is spun, the probability that it will land on 6 is still . The spinner landing on 6 for the previous 3 spins does not make it any more or less likely to land on 6 on the next spin.

1/3

1/2

1/4

The correct answer is 1/6 because there are 6 possible outcomes on the number cube and only 1 results in a 5. Each toss of the cube is an independent event, so the previous tosses do not affect the likelihood of getting a 5 on the next toss.

Explanation

The correct answer is 1/6 because there are 6 possible outcomes on the number cube and only 1 results in a 5. Each toss of the cube is an independent event, so the previous tosses do not affect the likelihood of getting a 5 on the next toss.

2. A banquet center offers a choice of 3 salads, 5 main courses and 4 desserts. How many different meals can be created by selecting one salad, one main course and one dessert?

12

20

Students need to recognize the situations when the Fundamental Counting Principle should be used to determine the total number of possible outcomes for situations. For example, Katie is making an ice cream sundae. She wants to make a sundae with 1 flavor of ice cream and 1 topping. She has 4 flavors of ice cream and 3 toppings to choose from. Students can use the Fundamental Counting Principle to solve this problem. To see why the principle works, consider the situation where Katie chooses vanilla ice cream. If she chooses vanilla ice cream, she can make three different kinds of sundaes. The same is true for each flavor of ice cream. She can also make three different kinds of sundaes with strawberry ice cream, with chocolate ice cream and with butter pecan ice cream. Therefore, if there are four different kinds of ice cream, and for each kind of ice cream there are three possible toppings, the total number of possible sundaes is .

35

The total number of different meals that can be created by selecting one salad, one main course, and one dessert is calculated by multiplying the number of choices for each category: 3 salads x 5 main courses x 4 desserts = 60 different meals.

Explanation

The total number of different meals that can be created by selecting one salad, one main course, and one dessert is calculated by multiplying the number of choices for each category: 3 salads x 5 main courses x 4 desserts = 60 different meals.

3. A store received a shipment of 64 boxes of crayons. The manager recorded how many boxes the store had left after each of 6 weeks. The data are shown in the scatterplot. The manager wants to predict how many boxes of crayons the store will have after the eighth week. Students can draw a line of best fit for the current data. The line should be as close to all the data points as possible. Assuming that the trend continues and using the line of best fit, students can now estimate that there will be about 24 boxes of crayons left after the eighth week.

The store will have more than 50 boxes of crayons left after the eighth week.

Students need to construct convincing arguments based on an analysis of data and interpretations of graphs. A store received a shipment of 64 boxes of crayons. The manager recorded how many boxes the store had left after each of 6 weeks. The data are shown in the scatterplot. The manager wants to predict how many boxes of crayons the store will have after the eighth week. Students can draw a line of best fit for the current data. The line should be as close to all the data points as possible. Assuming that the trend continues and using the line of best fit, students can now estimate that there will be about 24 boxes of crayons left after the eighth week.

The store will run out of crayons before the eighth week.

The store will only have 10 boxes of crayons left after the eighth week.

By drawing a line of best fit for the data and extrapolating to the eighth week, it is estimated that there will be about 24 boxes of crayons left. This prediction is based on the trend shown in the scatterplot.

Explanation

By drawing a line of best fit for the data and extrapolating to the eighth week, it is estimated that there will be about 24 boxes of crayons left. This prediction is based on the trend shown in the scatterplot.