Math Problem Statement
Solution
The problem is asking for the conditional probability that a student is a boy, given that they are a freshman.
To solve this, we use the formula for conditional probability:
Step 1: Find
From the table, the number of boys who are freshmen is 7.
Step 2: Find
The total number of freshmen (both boys and girls) is:
Step 3: Compute the conditional probability
Thus, the probability that a student is a boy, given that they are a freshman, is:
Would you like more details on this solution or have any questions?
Here are some related questions you might explore:
- What is the probability that a student is a girl, given that they are a freshman?
- What is the total probability that a randomly selected student is a boy?
- What is the probability that a student is a junior, given they are a boy?
- What is the probability that a student is a sophomore, given that they are a girl?
- How would the result change if more freshmen boys were added?
Tip: Conditional probability helps focus on a specific subgroup within the overall sample, making it useful in real-world situations where additional information is available.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Conditional Probability
Probability
Formulas
P(Boy | Freshman) = P(Boy and Freshman) / P(Freshman)
Theorems
Conditional Probability Formula
Suitable Grade Level
Grades 9-12
Related Recommendation
Conditional Probability: Finding the Probability of a Male Student Given Grade B
Exam Probability Calculations for Freshman and Sophomore Students
Probability with Freshman and Sophomore Students and Conditional Events
Calculate Conditional Probability for Male Students with Grade C
Conditional Probability: Finding Probability That a Student Is Male Given They Got an 'A'