As students were exiting the student center on campus, Vicki took note of whether they were listening to headphones. The table shows results that she collected.
Based on Vicki's data, what is the probability that a randomly selected student will have headphones in their ears when exiting the student center? Express your answer as a fraction in lowest terms or as a decimal rounded to the nearest millionth (if necessary).
Data for Students Exiting the Student Center
| | Number of Students |
| :-------------- | :------------------- |
| Headphones | 28 |
| No Headphones | 50 |
Answer (2)
The probability that a randomly selected student will have headphones when exiting the student center is approximately 0.358974. This is derived from a total of 78 students, with 28 using headphones. The fraction simplifies to 39 14 .
;
Calculate the total number of students: 28 + 50 = 78 .
Calculate the probability of a student having headphones: 78 28 = 39 14 .
Convert the fraction to a decimal rounded to the nearest millionth: 0.358974 .
The probability that a randomly selected student will have headphones is 0.358974 .
Explanation
Understand the problem We are given data about students exiting the student center, noting whether they have headphones. We need to find the probability that a randomly selected student has headphones.
Find the total number of students First, we need to find the total number of students observed. This is the sum of students with headphones and students without headphones.
Calculate the total The number of students with headphones is 28, and the number of students without headphones is 50. So, the total number of students is: 28 + 50 = 78
Calculate the probability Next, we calculate the probability of a student having headphones. This is the number of students with headphones divided by the total number of students.
Express as a fraction The probability of a student having headphones is: 78 28 = 39 14 Now, let's convert this fraction to a decimal rounded to the nearest millionth.
Convert to decimal 39 14 ≈ 0.35897435897 Rounding to the nearest millionth (6 decimal places), we get 0.358974.
Examples
Imagine you're organizing a school event and want to estimate how many students will need headphone-compatible audio guides. By calculating the probability of students using headphones based on past observations, you can better prepare the number of audio guides needed, ensuring a smoother experience for everyone.
