Given an experiment of drawing a miniature candy from a Halloween jar with 18 Snickers (made of nougat, caramel, peanuts), 16 3 Musketeers (made of nougat), and 21 Milky Way (made... Given an experiment of drawing a miniature candy from a Halloween jar with 18 Snickers (made of nougat, caramel, peanuts), 16 3 Musketeers (made of nougat), and 21 Milky Way (made of nougat, caramel) with events: N := the event "a miniature candy with nougat is drawn", R:= the event "a miniature candy with caramel is drawn", P := the event "a miniature candy without peanuts is drawn." 4. Construct a symbolic notation for the event "a miniature Milky Way is drawn." 5. Construct a verbal description for the the symbolic notation K = R complement union N.
Understand the Problem
The question presents a probability scenario involving drawing candy from a jar. It defines events N, R, and P based on the candy's ingredients (nougat, caramel, peanuts). Question 4 asks for the symbolic representation of the event of drawing a miniature Milky Way. Question 5 asks you to interpret the symbolic notation K = R complement union N in words
Answer
4. $N \cap R$ 5. A miniature candy without caramel is drawn, or a miniature candy with nougat is drawn, or both.
Answer for screen readers
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The symbolic notation for the event "a miniature Milky Way is drawn" is $N \cap R$.
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The verbal description for the symbolic notation $K = R^C \cup N$ is "a miniature candy without caramel is drawn, or a miniature candy with nougat is drawn, or both."
Steps to Solve
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Identify the ingredients of a Milky Way
A Milky Way contains nougat and caramel.
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Express "a miniature Milky Way is drawn" with the given events
Since N represents "a miniature candy with nougat is drawn" and R represents "a miniature candy with caramel is drawn", the event "a miniature Milky Way is drawn" can be represented as the intersection of these two events. The intersection of two events means both events occur.
Therefore, "a miniature Milky Way is drawn" is $N \cap R$.
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Understand the notation $R^C$
$R^C$ is the complement of R, meaning "a miniature candy without caramel is drawn."
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Understand the notation $R^C \cup N$
$R^C \cup N$ means the union of the events "a miniature candy without caramel is drawn" and ""a miniature candy with nougat is drawn". The union of two events means either one or both events can occur.
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Interpret $K = R^C \cup N$ verbally
$K = R^C \cup N$ can be described as "a miniature candy without caramel is drawn, or a miniature candy with nougat is drawn, or both."
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The symbolic notation for the event "a miniature Milky Way is drawn" is $N \cap R$.
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The verbal description for the symbolic notation $K = R^C \cup N$ is "a miniature candy without caramel is drawn, or a miniature candy with nougat is drawn, or both."
More Information
The intersection symbol $\cap$ represents "and," meaning both events must occur. The union symbol $\cup$ represents "or," meaning either one or both events can occur. The complement symbol $^C$ represents "not," meaning the event does not occur.
Tips
A common mistake for Question 4 is to use the union symbol $\cup$ instead of the intersection symbol $\cap$. Remember that a Milky Way must contain both nougat and caramel, so we need the intersection to represent "and."
A common mistake for Question 5 is to misinterpret the complement notation $R^C$. Remember that $R^C$ is everything that is not in R. Also important to remember that $R^C \cup N$ is the union, meaning either event or both, so the "both" must be stated.
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