To find out how many of the additional 1,000 voters will likely prefer Candidate 3 or Candidate 4, we need to calculate the probability of voters preferring Candidate 3 or Candidate 4.
Let event A be the event of preferring Candidate 3 and event B be the event of preferring Candidate 4.
We know that event A and event B are mutually exclusive events because a voter cannot prefer both Candidate 3 and Candidate 4. Therefore, the probability of voters preferring Candidate 3 or Candidate 4 is the sum of the probabilities of event A and event B occurring.
So, P(A or B) = P(A) + P(B)
From the table, we know that there are 450 supporters for Candidate 3 and 550 supporters for Candidate 4 out of 2,500 voters in the initial survey. Therefore, the probabilities of preferring Candidate 3 and Candidate 4 are:
P(A) = 450/2500 = 0.18
P(B) = 550/2500 = 0.22
Therefore, the probability of voters preferring Candidate 3 or Candidate 4 is:
P(A or B) = 0.18 + 0.22 = 0.40
So, out of the additional 1,000 voters surveyed, it is likely that approximately 40% of them or 400 voters will prefer Candidate 3 or Candidate 4.
Use what you have learned about mutually inclusive and exclusive events.
Apply the formula for calculating the probability of events A or B.
Question 1
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
b. If 1,000 more voters are surveyed, how many of them will likely prefer
Candidate 3 or 4? Explain the answer.
1 answer
1 answer