Identify Discrete Probability Distributions
-An Apple Pie Company Knows That $50 \%$

question 128

Multiple Choice

Identify Discrete Probability Distributions
-An Apple Pie Company knows that the number of pies sold each day varies from day to day. The owner believes that on $50 \%$ of the days she sells 100 pies. On another $25 \%$ of the days she sells 150 pies, and she sells 200 pies on the remaining $25 \%$ of the days. To make sure she has enough product, the owner bakes 200 pies each day at a cost of $\$ 1.50$ each. Assume any pies that go unsold are thrown out at the end of the day. If she sells the pies for $\$ 4$ each, find the probability distribution for her daily profit.

• A)
• \(\begin{array}{l|l}
• \text { Profit } & \mathrm{P} \text { (profit) } \\
• \hline \$ 100 & 0.5 \\
• \$ 300 & 0.25 \\
• \$ 500 & 0.25
• \end{array}\)
• B)
• \(\begin{array}{l|l}
• \text { Profit } & \text { P(profit) } \\
• \hline \$ 400 & 0.5 \\
• \$ 600 & 0.25 \\
• \$ 800 & 0.25
• \end{array}\)
• C)
• \(\begin{array}{l|l}
• \text { Profit } & \text { P(profit) } \\
• \hline \$ 200 & 0.5 \\
• \$ 400 & 0.25 \\
• \$ 600 & 0.25
• \end{array}\)
• D)
• \(\begin{array}{l|l}
• \text { Profit } & \text { P(profit) } \\
• \hline \$ 250 & 0.5 \\
• \$ 375 & 0.25 \\
• \$ 500 & 0.25
• \end{array}\)

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Definitions:

Disjunction

A logical operation that results in true if at least one of its component statements is true.

Self-Contradiction

A statement or proposition that inherently contradicts itself, making it logically impossible.

Biconditional

A logical statement that is true if both its components are either true or false together.

Self-Contradiction

Self-contradiction is a logical inconsistency whereby a statement contradicts itself directly or indirectly, rendering it logically impossible.