Consider the following information about a group of 119 FCC students:

Gender	Right-handed	Left-handed	Total
Female	41	12	53
Male	49	17	66
Total	90	29	119


If one person is randomly selected from the group, what is the probability that this student is female or right-handed?

To find the probability that a randomly selected student is either female or right-handed, we will use the principle of addition in probability.

Let:
- \( P(\text{Female}) \) be the probability of selecting a female.
- \( P(\text{Right-handed}) \) be the probability of selecting a right-handed student.
- \( P(\text{Female and Right-handed}) \) be the probability of selecting a student who is both female and right-handed.

The formula for the probability of \( A \) or \( B \) is:
\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

### Step 1: Find \( P(\text{Female}) \)
The number of females is 53 out of 119 total students, so:
\[
P(\text{Female}) = \frac{53}{119}
\]

### Step 2: Find \( P(\text{Right-handed}) \)
The number of right-handed students is 90 out of 119 total students, so:
\[
P(\text{Right-handed}) = \frac{90}{119}
\]

### Step 3: Find \( P(\text{Female and Right-handed}) \)
The number of students who are both female and right-handed is 41, so:
\[
P(\text{Female and Right-handed}) = \frac{41}{119}
\]

### Step 4: Calculate \( P(\text{Female or Right-handed}) \)
Now, we can apply the addition rule:
\[
P(\text{Female or Right-handed}) = P(\text{Female}) + P(\text{Right-handed}) - P(\text{Female and Right-handed})
\]
Substitute the values:
\[
P(\text{Female or Right-handed}) = \frac{53}{119} + \frac{90}{119} - \frac{41}{119}
\]
Simplifying the expression:
\[
P(\text{Female or Right-handed}) = \frac{53 + 90 - 41}{119} = \frac{102}{119}
\]

Thus, the probability that a randomly selected student is either female or right-handed is:
\[
\boxed{\frac{102}{119}} \approx 0.857
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What is the probability that a student is male or left-handed?
2. What is the probability that a student is both male and left-handed?
3. If two students are randomly selected, what is the probability that both are female?
4. What is the probability that a student is not right-handed?
5. What is the probability that a randomly selected student is both female and left-handed?

**Tip:** The principle of addition in probability helps avoid double-counting overlapping outcomes.

Consider the following information about a group of 119 FCC students: If one person is randomly selected from the group, what is the probability that this student is female or right-handed?

Learn how to calculate the probability of selecting a female or right-handed student from a group of 119 students using the addition rule in probability. Understand key concepts of probability and set theory, with detailed steps for solving the problem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation