Question

An administrator surveys a random sample of 48 out of 900 middle school

Answer 1

Considering the definition of probability, 12 of the 48 students surveyed were in favor of the new dress code.

Definition of probability

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

P(A)=number of favorable events÷ number of total events

Probability that students are in favor of the new dress code

In this case, you know:

• Total number of middle school students = 900 (number of possible cases)
• The number of students are in favor of the new dress code = 225 (number of favorable cases)

Replacing in the definition of probability:

P(A)=225 students÷ 900 students

Solving:

P(A)= 0.25

Expressed as a percentage:

P(A)= 25%

Number of the 48 students surveyed were that in favor of the new dress code

In this case, you know:

• Total number of middle school students = 48 (number of possible cases)
• 25% students are in favor of the new dress code (P(A)= 25%= 0.25)

Replacing in the definition of probability:

0.25=students in favor of the new dress code÷ 48 students

Solving:

students in favor of the new dress code= 0.25×48 students

students in favor of the new dress code= 12 students

Finally, 12 of the 48 students surveyed were in favor of the new dress code.

Learn more about probability:

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