Living Arrangements for Children Here are the living...

Living Arrangements for Children Here are the living arrangements of children under 18 years old living in the United States in a recent year. Numbers are in thousands. $$ \begin{array}{lc}{\text { Both parents }} & {51,823} \\ {\text { Mother only }} & {17,283} \\ {\text { Father only }} & {2,572} \\ {\text { Neither parent }} & {3,041}\end{array} $$ Choose one child at random; what is the probability that the child lives with both parents? With the mother present?

Living Arrangements for Children Here are the living arrangements of children under 18 years old living in the United States in a recent year. Numbers are in thousands.
$$
\begin{array}{lc}{\text { Both parents }} & {51,823} \\ {\text { Mother only }} & {17,283} \\ {\text { Father only }} & {2,572} \\ {\text { Neither parent }} & {3,041}\end{array}
$$
Choose one child at random; what is the probability that the child lives with both parents? With the mother present?

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Key Concepts

Relative Frequency

Relative frequency is a practical approach to estimating probability by using actual counts. It is computed as the number of times an event occurs divided by the total number of observations, representing the empirical probability of the event.

Addition Rule for Mutually Exclusive Events

The addition rule for mutually exclusive events states that if two events cannot occur at the same time, the probability that one or the other occurs is the sum of their individual probabilities. This rule is useful when calculating the probability of combined events that do not overlap.

Probability

Probability is a measure of how likely an event is to occur. It is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes, and it quantifies uncertainty in a precise mathematical way.

Sample Space

The sample space is the set of all possible outcomes of an experiment or scenario. In probability problems, every outcome must be included in the sample space, ensuring that the probabilities of all events sum to one.

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