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 variable whose value is subject to variation due to randomness or chance. It can take on different values depending on the outcome of a random process or experiment.
In the scenario described, you are conducting a survey to count the number of girls in families with five children. The number of girls in a family can vary from 0 (no girls, all boys) to 5 (all girls). Since the gender of each child is determined randomly (assuming each child has an equal chance of being a girl or a boy), the number of girls in a family is a result of a random process. Therefore, the number of girls in a family is subject to chance, and it can vary for each family.
This variability in the number of girls, depending on the random gender assignments for each of the five children, makes the count of girls a random variable.
Key Points:
- Random Process: The gender of each child is a random process, where each child has an equal probability of being a girl or a boy. Each child’s gender is independent of the others, meaning that the outcome for one child doesn’t affect the outcomes for the others.
- Range of Possible Outcomes: The number of girls can vary from 0 to 5, inclusive. This gives it a finite set of possible outcomes, which is a characteristic of discrete random variables.
- Random Variable Definition: A random variable must be defined as a numerical quantity that can take on different values depending on the outcome of a random experiment. In this case, the number of girls in the family is the result of a random experiment (assigning genders to the children), and it takes numerical values (0, 1, 2, 3, 4, or 5).
In conclusion, the number of girls in each family is a random variable because it is determined by a random process, and its value can vary from one family to another.