**Statistics grades:** In a statistics class of 

49

 students, there were 

11

 men and 

38

 women. Two of the men and three of the women received an A in the course. A student is chosen at random from the class.

(a) Find the probability that the student is a woman.

(b) Find the probability that the student received an A.

(c) Find the probability that the student is a woman or received an A.

(d) Find the probability that the student did not receive an A.

Let's solve each part of the problem step by step.

### (a) Probability that the student is a woman
The total number of students is \(49\), and the number of women is \(38\).

The probability that the student is a woman is given by:
\[
P(\text{Woman}) = \frac{\text{Number of women}}{\text{Total number of students}} = \frac{38}{49}
\]

### (b) Probability that the student received an A
The total number of students who received an A is the sum of the men and women who received an A:
\[
\text{Number of students who received an A} = 2 (\text{men}) + 3 (\text{women}) = 5
\]

The probability that the student received an A is:
\[
P(\text{A}) = \frac{\text{Number of students who received an A}}{\text{Total number of students}} = \frac{5}{49}
\]

### (c) Probability that the student is a woman or received an A
To find this probability, we need to use the formula for the union of two events:
\[
P(\text{Woman or A}) = P(\text{Woman}) + P(\text{A}) - P(\text{Woman and A})
\]

First, we calculate \(P(\text{Woman and A})\), which is the probability that the student is a woman who received an A:
\[
P(\text{Woman and A}) = \frac{\text{Number of women who received an A}}{\text{Total number of students}} = \frac{3}{49}
\]

Now, substituting the values:
\[
P(\text{Woman or A}) = \frac{38}{49} + \frac{5}{49} - \frac{3}{49} = \frac{40}{49}
\]

### (d) Probability that the student did not receive an A
The probability that the student did not receive an A is the complement of the probability that the student did receive an A:
\[
P(\text{Not A}) = 1 - P(\text{A}) = 1 - \frac{5}{49} = \frac{44}{49}
\]

### Summary of Probabilities
- **(a)** Probability that the student is a woman: \(\frac{38}{49}\)


Explore probability problems from a statistics class where you calculate the likelihood of selecting a woman, receiving an A grade, or both. Understand the concepts of probability and combinatorics with detailed solutions. Suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation