You decided to conduct a survey of families with five children. You are interested in counting the number of girls (out of five children) in each family. Is this a random variable?
A. Maybe
B. Cannot be determined
C. Yes, it is a random variable
D. No, it is not a random variable
The correct answer and explanation is :
The correct answer is C. Yes, it is a random variable.
Explanation:
A random variable is a numerical outcome of a random phenomenon. In this case, we are concerned with counting the number of girls in a family of five children. Since the number of girls can vary from family to family, and the outcome is determined by chance, it qualifies as a random variable. Let’s break this down:
- Definition of Random Variable: A random variable is a quantity whose value depends on the outcomes of a random process. This means the value is uncertain until the random process is carried out. Random variables can be either discrete (taking on specific, countable values) or continuous (taking on any value within a range).
- Context of the Question: The question involves counting the number of girls out of five children in each family. This is a countable quantity, as the number of girls can range from 0 (no girls) to 5 (all girls). Therefore, the possible values of this random variable are 0, 1, 2, 3, 4, and 5.
- Why It’s Random: The number of girls is determined by chance, as each child has an independent and random chance of being a girl or a boy. The process of determining how many girls there are in a family of five children is inherently random because it depends on the biological gender of each child, which is governed by probabilities that are not predictable with certainty for any given family.
- Why It’s a Discrete Random Variable: Since the number of girls can only take on whole number values between 0 and 5, it is a discrete random variable. It cannot take fractional values like 2.5 girls.
In conclusion, the number of girls in each family is a random variable because it is a countable, uncertain outcome influenced by random chance. Therefore, the correct answer is C. Yes, it is a random variable.