A family has two children. M represents male, and F represents female.
What is the sample space for the gender of the children?
{F, M}
{FM, FF, MM, MF} <my answer choice
{FF, MM}
{MF, FM}
looks good to me
The correct answer choice is {FM, FF, MM, MF}. This represents all possible combinations of the gender of the children: FM (first child is male, second child is female), FF (both children are female), MM (both children are male), and MF (first child is female, second child is male).
The sample space represents all possible outcomes of an event. In this case, the event is the gender of the children in a family with two children.
To determine the sample space, we can consider the possible combinations of genders for the two children.
Each child can be either male (M) or female (F). Since there are two children, the total number of possible outcomes is the number of combinations of two letters chosen from the set {M, F}.
Therefore, the correct answer is {FM, FF, MM, MF}. This represents all the possible combinations of genders for the two children: first child is female, second child is male (FM), both children are female (FF), both children are male (MM), and first child is male, second child is female (MF).