To determine the expected number of male students in a sample of 6, we use the concept of expected value in probability. The expected value of a random variable is the average or mean value that variable would take over an infinite number of trials.

In this case, we are dealing with the expected number of male students in a simple random sample of 6 students from a population of 18 males and 12 females (a total of 30 students).

The probability that any particular student chosen is male is:

$P(\text{male}) = \frac{18}{30} = 0.6$

Since the selection process is random and involves 6 students, the expected number of male students in the sample is given by:

$E(\text{male}) = \text{number of students} \times P(\text{male}) = 6 \times 0.6 = 3.6$

Thus, the expected number of male students in the sample of 6 is 3.6.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would the expected number change if there were more female students than male?
2. What is the probability of selecting exactly 4 males in the sample of 6?
3. How do we calculate the expected number of female students in the sample?
4. What if the sample size was increased to 10 students instead of 6? How does that affect the expected value?
5. What is the variance in the number of male students in the sample?

Tip: The expected value is linear, so even in more complex sampling situations, you can often simplify by focusing on individual probabilities.