Check for Understanding

Check for Understanding 1. You have a crazy die. It has sides of 0, 1, 2, 3, 4, and 5. Each has an even probability of being rolled. Let X = roll on this die X P(X)

0

1

2

3

4

5

a) Fill in the probabilities in the distribution above.

b) Determine the probability that you roll less than a 2 on this die. Write the probability statement first.

2. Choose an American household at random and let the random variable X be the number of cars (including SUVs and light trucks) they own. Here is a probability model if we ignore the few households that own more than 5 cars: Number of cars X: Probability:

0

1

2

3

4

5

0.09

0.36

0.35

0.13

0.05

0.02

(a) Say in words what the events {X > 1} is. Find P {X>1}. 3. A study of education followed a large group of fifth-grade children to see how many years of school they eventually completed. Let X be the highest year of school that a randomly chosen fifth-grader completes (Students who go on to college are included in the outcome X = 12.) The study found this probability distribution for X: Years 4 Probability: 0.010

5 0.007

6 0.007

7 0.013

8 0.032

(a) Find P (X > 6). (b) Find P (X > 6).

(c) Define and calculate another probability using this table.

9 0.068

10 0.070

11 0.041

12 0.752