Illinois State University Mathematics Department
MAT 312: Probability and Statistics for Middle School Teachers Spring 1999 
Quiz #4 look at solution notes 
1. TRUE or FALSE: Theoretical probability considers all possible things that could happen in an experiment. 

2. TRUE or FALSE: An experiment consists of flipping three coins and recording the number of heads. The sample space for the experiment is the set {1,2,3}. 

3. TRUE or FALSE: A fair die is rolled and the number on the faceup side is recorded, so the sample space is {1,2,3,4,5,6}. Each outcome in the sample space is equally likely. 

4. TRUE or FALSE: Two dice are rolled and the sum of the two faceup sides is recorded. Let event B represent that the sum is less than 5 and let event A represent that the sum is 7. Then P(B) = P(A). 

5. TRUE or FALSE: Two dice are rolled and the sum of the two faceup sides is recorded. If event X represents that the sum is not 7 and event Y represents that the sum is greater than or less than 7, X and Y are complementary events. 

6. TRUE or FALSE: Two coins are flipped and the number of tails is recorded. If event A represents that no tails appear and event B represents that two tails appear, A and B are mutually exclusive events. 

7. SOMETIMES TRUE, ALWAYS TRUE, or NEVER TRUE: If two events are complementary, then they are mutually exclusive. 

8. SOMETIMES TRUE, ALWAYS TRUE, or NEVER TRUE: An experiment consists of two tasks that involve a bag containing 3 green balls and 5 red balls. First, a ball is selected at random from the bag, the color of the ball is recorded, and the ball is placed in a waste can. Next, another ball is selected at random from the bag, the color of the ball is recorded, and this ball is placed in a waste can. If A represents the event "a red ball is selected" and B represents the event "a green ball is selected," then A and B are independent events. 

9. SOMETIMES TRUE, ALWAYS TRUE, or NEVER TRUE: Two events with the property that P(X) + P(Y) = 1 are complementary events. 

10. SOMETIMES TRUE, ALWAYS TRUE, or NEVER TRUE: For an experiment with the sample space {0,1,2}, P(0) = P(1) = P(2). 

11. A single letter is drawn from the set {g,e,o,m,t,r,y}. What is the probability that the letter drawn is a member of the set {g,e,o} ? 

12. An experiment consists of rolling a single fair die. Determine the probability that the result is: 

a) greater than 3. 
c) a number divisible by 6. 
b) a multiple of 5. 
d) a number divisible by 3 and 5. 
13. Two dice are rolled and the sum of the two faceup sides is recorded. What is the probability that one of the dice showed a "3" if we know that the sum was 7? 

14. Pat is about to take a 2item multiplechoice quiz. Each item has six possible answers (a,b,c,d,ef). Pat has no knowledge of the material and decides to roll a die to respond to each item. For multiplechoice question #1, if the die shows "1" Pat selects choice "a," if the die shows "2" Pat selects choice "b," and so on. Pat repeats this same dierolling activity to choose a response for multiplechoice question #2. What is the probability that Pat gets both questions correct on this quiz? 


Quiz Administered on Thursday 8 April 1999 . 