In the primary elections of a certain state, any candidate for governor must carry at least 55 percent of the counties in order to win the nomination out¬

right, without the necessity for a run-off election. A public opinion poll run on a sample of ten counties indicates that the candidate will carry only four of the ten. Assuming that the ten counties are a random sample of a large number of counties in the state, how probable is this result if the candidate will actually carry 55 percent of the counties? How probable is this result if he will actually carry 45 percent? Which of the two figures, 55 percent or 45 percent, is the better bet in the light of the evidence? Why?