A random selection of files from a student counseling center revealed the following reasons why college students seek services:
Mental health issues - 25
Learning/school issues - 15
Relationship issues - 5
Other - 5
What is the probability that if we pulled another student file from the counseling center the student would fall in each of the following categories a) mental health issues, b) learning/school issues OR relationship issues, c) any category except other?
To find the probability for each category, we need to calculate the ratio of the number of files in each category to the total number of files.
a) Probability of mental health issues:
There are 25 files with mental health issues out of a total of 50 files.
So, the probability that the next student file would fall into the mental health issues category is 25/50, which simplifies to 1/2 or 0.5.
b) Probability of learning/school issues OR relationship issues:
There are 15 files with learning/school issues and 5 files with relationship issues. To calculate the probability of either of these categories, we need to find the total number of files falling into these categories.
Total number of files with learning/school issues or relationship issues = 15 + 5 = 20
The probability that the next student file would fall into either the learning/school issues or relationship issues category is 20/50, which simplifies to 2/5 or 0.4.
c) Probability of any category except other:
There are 25 files with mental health issues, 15 files with learning/school issues, and 5 files with relationship issues, making a total of 45 files falling into these three categories.
The probability that the next student file would fall into any category except "other" is 45/50, which simplifies to 9/10 or 0.9.
So, the probabilities are as follows:
a) Probability of mental health issues: 0.5
b) Probability of learning/school issues OR relationship issues: 0.4
c) Probability of any category except other: 0.9
To calculate the probabilities, we need to determine the total number of files and the number of files in each category. Let's break it down:
a) Probability of a student having mental health issues:
Total number of files = 25 + 15 + 5 + 5 = 50
Number of files with mental health issues = 25
Probability = number of files with mental health issues / total number of files
Probability = 25 / 50 = 0.5
b) Probability of a student having learning/school issues OR relationship issues:
Total number of files = 50 (same as in part a)
Number of files with learning/school issues or relationship issues = 15 + 5 = 20
Probability = number of files with learning/school issues or relationship issues / total number of files
Probability = 20 / 50 = 0.4
c) Probability of a student falling into any category except "other":
Total number of files = 50 (same as in part a)
Number of files falling into any category except "other" = 25 + 15 + 5 = 45
Probability = number of files falling into any category except "other" / total number of files
Probability = 45 / 50 = 0.9
So, the probabilities are as follows:
a) Probability of a student having mental health issues = 0.5
b) Probability of a student having learning/school issues OR relationship issues = 0.4
c) Probability of a student falling into any category except "other" = 0.9