Questions: Debbie has two stocks, X and Y. Consider the following events: X= the event that the price of stock X has increased Y= the event that the price of stock Y has increased The event "the price of stock X has increased and the price of stock Y has not increased" may be written as Multiple Choice X' ∩ Y X or Y' X ∩ Y' X or Y

Solution Steps

To determine the correct representation of the event "the price of stock $X$ has increased and the price of stock $Y$ has not increased," we need to use set notation for events. The event that stock $X$ has increased is denoted by $X$, and the event that stock $Y$ has not increased is denoted by $Y^{\prime}$. The conjunction "and" in set notation is represented by the intersection symbol $\cap$. Therefore, the correct representation is $X \cap Y^{\prime}$.

Let \( X \) represent the event that the price of stock \( X \) has increased, and let \( Y \) represent the event that the price of stock \( Y \) has increased. The complement of \( Y \), denoted as \( Y' \), represents the event that the price of stock \( Y \) has not increased.

We are interested in the event where stock \( X \) has increased while stock \( Y \) has not increased. This can be expressed mathematically as the intersection of the events \( X \) and \( Y' \). Therefore, the event can be written as: \[ X \cap Y' \]

Among the given multiple-choice options, the correct representation of the event "the price of stock \( X \) has increased and the price of stock \( Y \) has not increased" is \( X \cap Y' \).

Final Answer