Use what you have learned about mutually inclusive and exclusive events. Apply the formula for calculating the probability of events A or B. There are four presidential candidates in a country. A street survey was conducted asking 2,500 registered voters which candidate they will vote for in the coming election. The table summarizes the results of the survey. Presidential Candidates Number of Supporters Candidate 1 250 Candidate 2 1,250 Candidate 3 450 Candidate 4 550 Part 1: What is the probability of randomly selecting a person who will vote for Candidate 1 or 2? (2 points) Responses 2502500 250 over 2500 15002500 1500 over 2500 10002500 1000 over 2500 12502500 1250 over 2500 Question 2 Part 2: If 1,000 more voters are surveyed, how many of them will likely prefer Candidate 3 or 4? Show your work and explain your answer.(2 points)
Part 1:
Probability of selecting a person who will vote for Candidate 1 or 2:
P(A or B) = P(A) + P(B) - P(A and B)
P(A) = Number of supporters for Candidate 1 / Total number of voters surveyed = 250 / 2500 = 0.1
P(B) = Number of supporters for Candidate 2 / Total number of voters surveyed = 1250 / 2500 = 0.5
P(A and B) = 0 (since a person cannot support both Candidate 1 and 2)
P(A or B) = 0.1 + 0.5 - 0 = 0.6
Therefore, the probability of randomly selecting a person who will vote for Candidate 1 or 2 is 0.6.
Part 2:
If 1,000 more voters are surveyed, we can apply the formula for calculating the probability of events A or B:
P(A or B) = P(A) + P(B) - P(A and B)
P(C) = Number of supporters for Candidate 3 / Total number of voters surveyed = 450 / 3500 = 0.1286
P(D) = Number of supporters for Candidate 4 / Total number of voters surveyed = 550 / 3500 = 0.1571
P(C and D) = 0 (since a person cannot support both Candidate 3 and 4)
P(C or D) = 0.1286 + 0.1571 - 0 = 0.2857
Therefore, out of the additional 1,000 voters surveyed, approximately 286 will likely prefer Candidate 3 or 4.