Questions: Question 17 2 pts (CO 2) A statistics class has 50 students and among those students, 35 are business majors and 8 like grilled cheese. Of the business majors, 3 like grilled cheese. Find the probability that a randomly selected statistics student is a business major or likes grilled cheese. 0.94 0.96 0.80 0.84

Question 17 2 pts (CO 2) A statistics class has 50 students and among those students, 35 are business majors and 8 like grilled cheese. Of the business majors, 3 like grilled cheese. Find the probability that a randomly selected statistics student is a business major or likes grilled cheese. 0.94 0.96 0.80 0.84
Transcript text: Question 17 2 pts (CO 2) A statistics class has 50 students and among those students, 35 are business majors and 8 like grilled cheese. Of the business majors, 3 like grilled cheese. Find the probability that a randomly selected statistics student is a business major or likes grilled cheese. 0.94 0.96 0.80 0.84
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Solution

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Solution Steps

Step 1: Identify the given information
  • Total number of students: \( n = 50 \)
  • Number of business majors: \( \text{Business} = 35 \)
  • Number of students who like grilled cheese: \( \text{Grilled Cheese} = 8 \)
  • Number of business majors who like grilled cheese: \( \text{Business} \cap \text{Grilled Cheese} = 3 \)
Step 2: Calculate the probability of being a business major

The probability of a student being a business major is: \[ P(\text{Business}) = \frac{\text{Number of business majors}}{\text{Total number of students}} = \frac{35}{50} \]

Step 3: Calculate the probability of liking grilled cheese

The probability of a student liking grilled cheese is: \[ P(\text{Grilled Cheese}) = \frac{\text{Number of students who like grilled cheese}}{\text{Total number of students}} = \frac{8}{50} \]

Step 4: Calculate the probability of being a business major and liking grilled cheese

The probability of a student being a business major and liking grilled cheese is: \[ P(\text{Business} \cap \text{Grilled Cheese}) = \frac{\text{Number of business majors who like grilled cheese}}{\text{Total number of students}} = \frac{3}{50} \]

Step 5: Apply the addition rule for probabilities

The probability of a student being a business major or liking grilled cheese is: \[ P(\text{Business} \cup \text{Grilled Cheese}) = P(\text{Business}) + P(\text{Grilled Cheese}) - P(\text{Business} \cap \text{Grilled Cheese}) \] Substitute the values: \[ P(\text{Business} \cup \text{Grilled Cheese}) = \frac{35}{50} + \frac{8}{50} - \frac{3}{50} = \frac{40}{50} = 0.80 \]

Step 6: Match the result with the given options

The calculated probability \( 0.80 \) matches one of the provided options.

Final Answer

\(\boxed{0.80}\)

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