Question

Use what you have learned about mutually inclusive and exclusive events.
Apply the formula for calculating the probability of events A or B.
Lesson
Note
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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.

Answer 1

Candidate A B C D Total
Number of Voters 800 600 700 400 2,500

If we want to calculate the probability of a voter selecting Candidate A or Candidate B, we need to consider that these events are mutually inclusive, as a voter can select both candidates.

The formula for calculating the probability of events A or B is:
P(A or B) = P(A) + P(B) - P(A and B)

First, let's calculate the probability of selecting Candidate A:
P(A) = Number of voters selecting Candidate A / Total number of voters
P(A) = 800 / 2,500 = 0.32

Next, let's calculate the probability of selecting Candidate B:
P(B) = Number of voters selecting Candidate B / Total number of voters
P(B) = 600 / 2,500 = 0.24

Now, let's calculate the probability of selecting both Candidate A and Candidate B:
P(A and B) = Number of voters selecting both A and B / Total number of voters
P(A and B) = 0

Since the events of selecting Candidate A and Candidate B are mutually inclusive, the probability of selecting either A or B is:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.32 + 0.24 - 0
P(A or B) = 0.56

Therefore, the probability of a voter selecting Candidate A or Candidate B in the coming election is 0.56.