Illinois State University Mathematics Department

 MAT 312: Probability and Statistics for Middle School Teachers Dr. Roger Day (day@ilstu.edu)

### Assignment #4

possible solutions

Assignment due on Tuesday, 7/6/04

1. If Sanchez is scheduled to play Novatna in the next tournament, what is the probability Sanchez will win?

2. Which player-to-player match-up indicates the least probable chance of winning? Who is the player with the least probable chance and what is the probability she will win?

B. All automobile license plates in Liberia have six characters. The characters can be letters of the alphabet (A, B, . . . , Z) or single-digit numbers (0, 1, . . . , 9).

3. If a license plate has four letters followed by two digits, with repetition allowed, how many different license plates are possible?

4. If a license plate again has four letters followed by two digits, this time with repetition not allowed, how many different license plates are possible?

5. If a license plate has three letters followed by three digits, with no repetitions allowed and no use of either the letter O or the digit 0, how many different license plates are possible?

C. From a class of 20 students, a committee of 3 is to be formed to organize a fundraiser.

6. If all 20 students are eligible for committee membership, how many different committees could be formed?

7. If there are 12 women and 8 men in the class, and the committee requires at least one member of each gender, how many different committees could be formed?

D. For each situation below, determine whether the description represents a discrete random variable, a continuous random variable, or neither. Explain your choice.

8. The number of tacks that land head flat when 20 tacks are tossed on to a flat surface.

9. The length of time the department office must wait until its copy machine is repaired.

10. The height of students in a suburban elementary school.

11. The number of times an employee is late during each monthly pay period.

12. The number of blue tokens in a bag that contains 40 blue tokens.

E. Many states have their own lotteries, games of chance where people buy tickets and select numbers and check whether their selected numbers match the numbers selected at random by the state. One of the games in the Big Mountain lottery is a 3-digit game, where players spend \$1 to select a three-digit number (repeats allowed).

13. A wager of \$1 buys a single play, composed of one three-digit combination. How many different three-digit combinations are possible in this version of the lottery? Note that the selection 3 2 2 is different from the selection 2 3 2.

14. For this version of the lottery, what is the probability of winning on a single \$1 play?

15. Consider the possible lottery winnings as a random variable x, knowing that on a successful \$1 play, a winner gets \$500.

(i) Show the distribution of the random variable x.

(ii) Determine the expected value of x.

(iii) Is this version of the lottery a fair game? Explain.

F. The random variable v has the following discrete probability distribution:

 v 0 1 2 3 4 p(v) 0.2 0.1 0.4 0.1 0.2

16. Determine these values:

(i) P(v = 2)

(ii) P(v is less than or equal to 3)

(iii) P(w > 2)

17. Determine the expected value of v.

18. Graph p(v), the discrete probability distribution.

19. Identify a random variable and then create a table to show the discrete probability distribution for the outcomes of this situation:

Two fair dice are rolled and the sum of the values on the face-up sides is noted.

BONUS! NOT A REQUIRED PROBLEM!

Suppose the four players listed with questions 1 and 2 are the only entries in a single-elimination championship tournament. Here are the pairings for the first round matches:

Match #1: Sanchez vs Graf

Match #2: Novatna vs Sabatini

The winners of these two matches play a third match for the championship. For each player, determine her probability of winning the tournament.