Question 1:

A tetrahedron is a fully-symmetric pyramid-like solid, with four faces made up of equal-sized equilateral triangles. Suppose that the four faces contain different number of spots, from one spot to four spots, so that the tetrahedron may be rolled as a die. The number of spots which results from the roll of this die is the number of spots on the bottom face, the one which can not be seen. In the example, the die has thrown a two.

a. Suppose two such dice are rolled. Write a list of all possible equally-likely pairs of numbers of spots which could result.

b. If two such dice are rolled, what is the probability that the sum of the spots will be four?

c. If two such dice are rolled, what is the probability that the sum of the spots will be greater than two?

Question 2:

Prior to an election, campaign committees or news organizations sometimes pay for an opinion poll of prospective voters. Suppose that a newspaper reports that, if the election were held now, 52% of voters would vote for candidate X, with a margin of error of plus or minus 3%.

a. If no confidence level is reported for the result, what is the assumed level?

b. What is the minimum number of randomly-selected prospective votes who needed to be polled in order to achieve the level of confidence you assumed in part (a)?

c. Suppose that the poll was conducted as you specified in part (b). Explain what difference it would make to your confidence in the statement "52% + 3% of voters would choose candidate X," if the poll were used to predict a local election, versus a national one.

d. Discuss whether the poll result implies that candidate X will win a majority of the votes.