At a local college, 480 of the male students are smokers and 520 are non-smokers. Of the female students, 101 are smokers and 909 are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers?
Do not round your answer.

To find the probability that both a randomly selected male student and a randomly selected female student are smokers, we need to follow these steps:

### Step 1: Calculate the total number of male students.
The total number of male students is the sum of smokers and non-smokers:
\[
480 + 520 = 1000
\]

### Step 2: Calculate the total number of female students.
The total number of female students is also the sum of smokers and non-smokers:
\[
101 + 909 = 1010
\]

### Step 3: Calculate the probability that the male student selected is a smoker.
The probability that a randomly selected male student is a smoker is:
\[
\frac{480}{1000} = \frac{24}{50}
\]

### Step 4: Calculate the probability that the female student selected is a smoker.
The probability that a randomly selected female student is a smoker is:
\[
\frac{101}{1010} = \frac{101}{1010}
\]

### Step 5: Calculate the probability that both the male and female students selected are smokers.
Since the selection of the male and female students are independent events, the probability that both are smokers is the product of the individual probabilities:
\[
\text{Probability} = \left(\frac{24}{50}\right) \times \left(\frac{101}{1010}\right)
\]

Simplifying the product:
\[
\text{Probability} = \frac{24 \times 101}{50 \times 1010} = \frac{2424}{50500}
\]

The fraction \(\frac{2424}{50500}\) is already in its simplest form, so the probability that both selected students are smokers is:
\[
\frac{2424}{50500}
\]

Would you like more details or have any questions?

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Here are 8 related questions to consider:

1. What is the probability that both selected students are non-smokers?
2. How would the probability change if the number of female smokers increased by 50?
3. What is the probability that exactly one of the selected students is a smoker?
4. How can this problem be extended to more than two students being selected?
5. What is the probability that neither of the selected students is a smoker?
6. How does the concept of independence affect the calculation of combined probabilities?
7. What if the number of male non-smokers doubled? How would that affect the result?
8. Can you calculate the odds in favor of both students being smokers?

**Tip:** When dealing with probabilities involving independent events, remember that you can simply multiply the probabilities of each individual event.

Explore the probability of randomly selecting both a male and a female smoker from a college survey. Understand how to calculate probabilities of independent events and apply them to real-world data. Detailed step-by-step solution included.

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