Questions: A probability experiment is conducted in which the sample space of the experiment is S=5,6,7,8,9,10,11,12,13,14,15,16, event F=5,6,7,8,9,10, and event G=9,10,11,12. Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule. A. F or G=5,6,7,8,9,10,11,12 (Use a comma to separate answers as needed.) B. F or G= Find P(F or G) by counting the number of outcomes in F or G. P(F or G)=0.667 (Type an integer or a decimal rounded to three decimal places as needed.) Determine P(F or G) using the general addition rule. Select the correct choice below and fill in any answer boxes within your choice. (Type the terms of your expression in the same order as they appear in the original expression. Round to three decimal places as needed.) A. P(F or G)= + = B. P(F or G)= =

A probability experiment is conducted in which the sample space of the experiment is S=5,6,7,8,9,10,11,12,13,14,15,16, event F=5,6,7,8,9,10, and event G=9,10,11,12. Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule. A. F or G=5,6,7,8,9,10,11,12 (Use a comma to separate answers as needed.) B. F or G= Find P(F or G) by counting the number of outcomes in F or G. P(F or G)=0.667 (Type an integer or a decimal rounded to three decimal places as needed.) Determine P(F or G) using the general addition rule. Select the correct choice below and fill in any answer boxes within your choice. (Type the terms of your expression in the same order as they appear in the original expression. Round to three decimal places as needed.) A. P(F or G)= + = B. P(F or G)= =
Transcript text: A probability experiment is conducted in which the sample space of the experiment is $S=\{5,6,7,8,9,10,11,12,13,14,15,16\}$, event $F=\{5,6,7,8,9,10\}$, and event $G=\{9,10,11,12\}$. Assume that each outcome is equally likely. List the outcomes in F or G . Find $\mathrm{P}(\mathrm{F}$ or G$)$ by counting the number of outcomes in F or G. Determine P(F or $G)$ using the general addition rule. A. F or $\mathrm{G}=\{5,6,7,8,9,10,11,12\}$ (Use a comma to separate answers as needed.) B. $F$ or $G=\{ \}$ Find $P(F$ or $G)$ by counting the number of outcomes in $F$ or $\mathbf{G}$. \[ P(F \text { or } G)=0.667 \] (Type an integer or a decimal rounded to three decimal places as needed.) Determine $\mathrm{P}(\mathrm{F}$ or G$)$ using the general addition rule. Select the correct choice below and fill in any answer boxes within your choice. (Type the terms of your expression in the same order as they appear in the original expression. Round to three decimal places as needed.) A. $P(F$ or $G)=$ $\square$ $+\square$ $\square$ $\square=$ $\square$ B. $P(F$ or $G)=$ $\square$ $\square$ $=\square$
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Solution

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Solution Steps

Step 1: List the outcomes in \( F \) or \( G \)

The outcomes in \( F \) or \( G \) are the union of the sets \( F \) and \( G \). Given:

  • \( F = \{5, 6, 7, 8, 9, 10\} \)
  • \( G = \{9, 10, 11, 12\} \)

The union \( F \cup G \) is: \[ F \cup G = \{5, 6, 7, 8, 9, 10, 11, 12\} \]

Thus, the correct answer is: \[ \boxed{F \text{ or } G = \{5, 6, 7, 8, 9, 10, 11, 12\}} \]

Step 2: Find \( P(F \text{ or } G) \) by counting the number of outcomes in \( F \) or \( G \)

The total number of outcomes in the sample space \( S \) is 12. The number of outcomes in \( F \cup G \) is 8. Therefore, the probability \( P(F \text{ or } G) \) is: \[ P(F \text{ or } G) = \frac{\text{Number of outcomes in } F \cup G}{\text{Total number of outcomes in } S} = \frac{8}{12} = 0.6667 \]

Rounded to three decimal places: \[ \boxed{P(F \text{ or } G) = 0.667} \]

Step 3: Determine \( P(F \text{ or } G) \) using the general addition rule

The general addition rule states: \[ P(F \text{ or } G) = P(F) + P(G) - P(F \cap G) \]

First, calculate \( P(F) \), \( P(G) \), and \( P(F \cap G) \):

  • \( P(F) = \frac{\text{Number of outcomes in } F}{\text{Total number of outcomes in } S} = \frac{6}{12} = 0.5 \)
  • \( P(G) = \frac{\text{Number of outcomes in } G}{\text{Total number of outcomes in } S} = \frac{4}{12} = 0.3333 \)
  • \( P(F \cap G) = \frac{\text{Number of outcomes in } F \cap G}{\text{Total number of outcomes in } S} = \frac{2}{12} = 0.1667 \)

Substitute these values into the general addition rule: \[ P(F \text{ or } G) = 0.5 + 0.3333 - 0.1667 = 0.6666 \]

Rounded to three decimal places: \[ \boxed{P(F \text{ or } G) = 0.667} \]

Final Answer

  1. \( \boxed{F \text{ or } G = \{5, 6, 7, 8, 9, 10, 11, 12\}} \)
  2. \( \boxed{P(F \text{ or } G) = 0.667} \)
  3. \( \boxed{P(F \text{ or } G) = 0.667} \)
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