Question

twila zone asked students to name their favorite radio station.

1. what will be the size of the sample space when calculating the probability?
2. based on the data, what is the probability that a randomly selected students favorite radio station would be:

wrok
wrap
not whit

1. if there are 1260 students at twilas school, about how many of them would you expect to choose wrok?

Explanation:

Step1: Calculate the total number of students (sample space size)

$$33 + 56+9 + 24=122$$

Step2: Calculate probability for WROK

Probability \(P(\text{WROK})=\frac{\text{Number of students for WROK}}{\text{Total number of students}}=\frac{33}{122}\)

Step3: Calculate probability for WRAP

Probability \(P(\text{WRAP})=\frac{\text{Number of students for WRAP}}{\text{Total number of students}}=\frac{56}{122}=\frac{28}{61}\)

Step4: Calculate probability for NOT WHIT

Number of students not for WHIT \(=122 - 9=113\)
Probability \(P(\text{NOT WHIT})=\frac{113}{122}\)

Step5: Calculate expected number for WROK in 1260 students

Let \(x\) be the expected number. Using proportion \(\frac{33}{122}=\frac{x}{1260}\)
Cross - multiply: \(122x=33\times1260\)
\(x=\frac{33\times1260}{122}=\frac{41580}{122}\approx341\)

Answer:

1. The size of the sample space is \(122\).

14.

• Probability for WROK: \(\frac{33}{122}\)
• Probability for WRAP: \(\frac{28}{61}\)
• Probability for NOT WHIT: \(\frac{113}{122}\)

1. Approximately \(341\) students.