Question: In some countries there are no primary elections to narrow down the field of candidates, so several candidates could run for a particular office. If a candidate does not receive a majority, then the two candidates with the most votes run against each other in a runoff election a few weeks later. Suppose that three candidates - Candidate A, Candidate B. and Candidate C - are running from three different regions of the country - Region 1. Region 2, and Region 3.

Candidate A is from Region 1. Based on previous results. Region 1 costs about 35% of all votes in the country. Polls indicate that Region 1 will cast about 70% of its votes for candidate A, 20% for Candidate B, and 10% for Candidate C.

Candidate B is from Region 2. Based on previous results, Region 2 casts about 50% of all votes in the country. Polls indicate that Regions 2 will cast about 20% of its votes for candidate A. 60% for Candidate B, and 20% for Candidate C.

Candidate C is from Region 3. Based on previous results. Region 3 casts about 15% of all votes in the country. Polls indicate that Region 3 will cast about 25% of its votes for candidate A, 15% for Candidate B, and 60% for Candidate C.

(A) If the actual vote is in line with the preliminary estimates, will one of the candidates receive a majority of the votes. If not, which two candidates will be in the runoff election? Show your work that leads to your conclusion.

(B) What proportion of her total vote did Candidate C receive from her home region?