Questions: A probability experiment is conducted in which the sample space of the experiment is S=3,4,5,6,7,8,9,10,11,12,13,14, event F=3,4,5,6,7, and event G=7,8,9,10. 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. List the outcomes in F or G. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. F or G= (Use a comma to separate answers as needed.) B. F or G=

A probability experiment is conducted in which the sample space of the experiment is S=3,4,5,6,7,8,9,10,11,12,13,14, event F=3,4,5,6,7, and event G=7,8,9,10. 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. List the outcomes in F or G. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. F or G= (Use a comma to separate answers as needed.) B. F or G=
Transcript text: A probability experiment is conducted in which the sample space of the experiment is $S=\{3,4,5,6,7,8,9,10,11,12,13,14\}$, event $F=\{3,4,5,6,7\}$, and event $G=\{7,8,9,10\}$. 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. List the outcomes in F or G. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. F or $\mathrm{G}=$ $\square$ \} (Use a comma to separate answers as needed.) B. F or $\mathrm{G}=\{ \}$
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Solution

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Solution Steps

Step 1: List the Union of Events F and G

The union of events F and G is: {3, 4, 5, 6, 7, 8, 9, 10}

Step 2: Count the Number of Outcomes in F U G

The number of outcomes in F U G is: 8

Step 3: Calculate the Probability of F U G

The probability of F U G is: $P(F \cup G) = \frac{8}{12} = 0.67$

Step 4: Apply the General Addition Rule

Using the general addition rule, $P(F \cup G) = P(F) + P(G) - P(F \cap G) = \frac{5}{12} + \frac{4}{12} - \frac{1}{12} = 0.67$

Final Answer:

The probability of the union of events F and G is: 0.67

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