The U.S. Census Bureau provides data on the number of young...

The U.S. Census Bureau provides data on the number of young adults, ages $18-24,$ who are living in their parents' home. Let $$\begin{aligned} M &=\text { the event a male young adult is living in his parents' home } \\ F &=\text { the event a female young adult is living in her parents' home } \end{aligned}$$ If we randomly select a male young adult and a female young adult, the Census Bureau data enable us to conclude $P(M)=.56$ and $P(F)=.42$ (The World Almanac, $2006 ) .$ The probability that both are living in their parents' home is 24 . $\begin{array}{l}{\text { a. What is the probability at least one of the two young adults selected is living in his or }} \\ {\text { her parents' home? }}\end{array}$ $\begin{array}{l}{\text { b. What is the probability both young adults selected are living on their own (neither is }} \\ {\text { living in their parents' home)? }}\end{array}$

The U.S. Census Bureau provides data on the number of young adults, ages $18-24,$ who
are living in their parents' home. Let
$$\begin{aligned} M &=\text { the event a male young adult is living in his parents' home } \\ F &=\text { the event a female young adult is living in her parents' home } \end{aligned}$$
If we randomly select a male young adult and a female young adult, the Census Bureau
data enable us to conclude $P(M)=.56$ and $P(F)=.42$ (The World Almanac, $2006 ) .$ The
probability that both are living in their parents' home is 24 .
$\begin{array}{l}{\text { a. What is the probability at least one of the two young adults selected is living in his or }} \\ {\text { her parents' home? }}\end{array}$
$\begin{array}{l}{\text { b. What is the probability both young adults selected are living on their own (neither is }} \\ {\text { living in their parents' home)? }}\end{array}$

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Key Concepts

Joint Probability

Joint probability refers to the probability of two events occurring together. In problems involving two events, knowing the joint probability is essential for applying the inclusion-exclusion principle and for determining overall probabilities in scenarios where events might overlap.

Complement Rule

The complement rule is used to determine the probability that an event does not occur. It states that the probability of the complement of an event is equal to one minus the probability of the event. This concept is useful for finding the probability of neither event occurring by subtracting the probability of at least one event occurring from one.

Inclusion-Exclusion Principle

This principle is used to calculate the probability of the union of two events. It states that the probability that at least one of two events occurs is equal to the sum of their individual probabilities minus the probability of their intersection. This is crucial when accounting for any overlap between events.

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