Question

10 multiple choice 4 points
three high school juniors, reese, matthew, and chris, are running for student council president. a survey is taken a week before the election asking 40 students which candidate they will vote for in the election. the results are shown in the table below.
based on the table, what is the probability that a student will vote for reese?
11 multiple choice 4 points
from a standard deck of 52 cards, one card is drawn. what is the probability that it will be either a club or a diamond?

Explanation:

Step1: Calculate total number of students

Total number of students surveyed is \(15 + 13+12=40\)

Step2: Calculate probability for Reese

Probability \(P=\frac{\text{Number of students for Reese}}{\text{Total number of students}}\). So \(P = \frac{15}{40}=\frac{3}{8}\)

Step3: Calculate number of club and diamond cards

In a standard deck, there are 13 club cards and 13 diamond cards. So total number of club or diamond cards is \(13 + 13=26\)

Step4: Calculate probability for club or diamond

Probability \(P=\frac{\text{Number of club or diamond cards}}{\text{Total number of cards}}\). So \(P=\frac{26}{52}=\frac{1}{2}\) (but let's check the options. The formula is correct as \(\frac{26}{52}\) is an option)

Answer:

For the first question (Reese's probability): \(\frac{3}{8}\) (third option).
For the second question (club or diamond probability): \(\frac{26}{52}\) (third option).