To find the probability that a student selected at random is male and motivated primarily by money, we need to follow these steps:
### Step 1: Understand the Problem
We are given a table with the categorization of students according to gender and primary career motivation. Our task is to determine the probability of selecting a male student whose primary career motivation is money.
### Step 2: Identify the Relevant Information
From the table, we can extract the relevant data:
- Number of male students motivated primarily by money: \(15\)
- Total number of students: \(100\)
### Step 3: Use the Probability Formula
The probability \(P(E)\) of an event \(E\) occurring is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this context:
[tex]\[
P(\text{Male and motivated by money}) = \frac{\text{Number of male students motivated by money}}{\text{Total number of students}}
\][/tex]
### Step 4: Substitute the Values
Substituting the values from the table:
[tex]\[
P(\text{Male and motivated by money}) = \frac{15}{100}
\][/tex]
### Step 5: Simplify the Fraction
Simplify the fraction \(\frac{15}{100}\):
[tex]\[
\frac{15}{100} = \frac{3}{20}
\][/tex]
### Step 6: State the Answer
The probability that a student selected at random is a male and motivated primarily by money is:
[tex]\[
\boxed{\frac{3}{20}}
\][/tex]
This fraction is already in its simplest form. So, the final answer is [tex]\(\frac{3}{20}\)[/tex].
