# MATHEMATICS

9. A bag contains four chips of which one is red, one is blue, one is green, and one is yellow. A chip is selected at random from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of the possible outcomes (for example, RB represents the outcome red chip followed by blue chip) and use your list to determine the probability that the two chips selected are the same color. (Hint: There are 16 possible outcomes.)A. 1/4 B. ¾ C. 2/16 D. 3/16

Possible outcomes: RR RB RG RY

BR BB BG BY

GR GB GG GY

YR YB YG YY

P(two of same color) = (Number of combinations with same color) / (Total

number of combinations)

P(two of same color) = 4/16 = ¼

10. A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.)A. 0.6 B. 0.4 C. 0.7 D. 0.8

Sample space: ABC ABD ABE ACD ACE

ADE BCD BCE BDE CDE

P(combination includes B) = (Number of combinations including B) / (Total

number of combinations)

P(combination includes B) = 6/10 = 0.6

11. In the first series of rolls of a die, the number of odd numbers exceeded the number of even numbers by 5. In the second series of rolls of the same die, the number of odd numbers exceeded the number of even numbers by 11. Determine which series is closer to the 50/50 ratio of odd/even expected of a fairly rolled die.

A. The second series is closer because the difference between odd and even numbers is greater than the difference for the first series.

B. The first series is closer because the difference between odd and even numbers is less than the difference for the second series.

C. Since 1/2 > 1/5 > 1/11, the first series is closer.

D. The series closer to the theoretical 50/50 cannot be determined unless the total number of rolls for both series is given.

12. Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio of odd/even expected of such a series of temperature checks.

A. The Monday series is closer because 1/6 is closer to 1/2 than is 1/8.

B. The Monday series is closer because 6/12 is closer to 0.5 than is 8/18.

C. The Tuesday series is closer because the 13/18 is closer to 0.5 than is 9/12.

D. The series closest to the theoretical 50/50 cannot be determined without knowing the number of odds and evens in each series.

Monday: 9 odd, 3 even P(odd) = 9/12 = 0.75

Tuesday: 13 odd, 5 even P(odd) = 13/18 ≈ 0.722 < 0.75

13. Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 5 or a 2, nothing otherwise. What is your expected value?

A. $1.00 B. $0.00 C. $3.00 D. −$1.00

E(x) = (1/3)($3) – $1 = $1 – $1 = $0