Questions: The table below shows the soft drinks preferences of people in three age groups. If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer given that they are over 40 - Cola Root Beer Lemon-lime Under 21 years of age 40 25 20 Between 21 and 40 35 20 30 Over 40 years of age 20 30 35 A. 2/5 B. 6/17 C. 2/17 D. None of the above

Solution Steps

To find the probability that a person drinks root beer given that they are over 40, we need to use conditional probability. First, determine the total number of people over 40, then find how many of those people prefer root beer. The probability is the ratio of these two numbers.

From the data provided, the number of people over 40 who prefer each type of drink is as follows:

• Cola: \(20\)
• Root Beer: \(30\)
• Lemon-lime: \(35\)

Thus, the total number of people over 40 is calculated as: \[ \text{Total}_{\text{over 40}} = 20 + 30 + 35 = 85 \]

The number of people over 40 who prefer root beer is given as: \[ \text{Root Beer}_{\text{over 40}} = 30 \]

The probability that a randomly selected person drinks root beer given that they are over 40 is given by the formula: \[ P(\text{Root Beer} \mid \text{Over 40}) = \frac{\text{Root Beer}_{\text{over 40}}}{\text{Total}_{\text{over 40}}} \] Substituting the values: \[ P(\text{Root Beer} \mid \text{Over 40}) = \frac{30}{85} \approx 0.3529 \]

Final Answer