Illinois State University Mathematics Department

MAT 312: Probability and Statistics for Middle School Teachers

Spring 1999
9:35 - 10:50 am TR STV 350A
Dr. Roger Day (day@math.ilstu.edu)



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 face-up 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 face-up 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 face-up 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 face-up 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 2-item multiple-choice 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 multiple-choice 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 die-rolling activity to choose a response for multiple-choice question #2.

What is the probability that Pat gets both questions correct on this quiz?

15. An experiment consists of throwing two darts at the board shown to the right and recording the sum of the numbers showing within the regions hit by the darts.

For example, if one dart hits the upper-right sector of the circle and the other dart hits the lower-left sector, a sum of 8 is recorded. If both darts hit the lower-right sector, a sum of 16 is recorded.

Assume that each dart hits somewhere on the board and that each of the four sectors of the board represent one-fourth of a circle.

a) List the sample space for this experiment.

b) Determine P(12) for this experiment.

c) Determine P(10 | one dart hits a 6).



Quiz Administered on Thursday 8 April 1999
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