To find the probability that a randomly chosen person from the group likes apple juice, we need to know how many people like apple juice out of the total surveyed.
From the survey:
- Total people surveyed: 150
- People who like apple juice: 65
- People who dislike apple juice: 85
Now, let's check if the numbers add up: 65 (like) + 85 (dislike) = 150 (total), which is correct.
The probability (P) that a randomly selected person likes apple juice can be calculated as:
\[ P(\text{likes apple juice}) = \frac{\text{Number of people who like apple juice}}{\text{Total number of people surveyed}} = \frac{65}{150} \]
Now, we simplify the fraction \( \frac{65}{150} \):
- The greatest common divisor (GCD) of 65 and 150 is 5.
- Dividing both the numerator and the denominator by 5:
\[ \frac{65 \div 5}{150 \div 5} = \frac{13}{30} \]
Thus, the probability that a randomly selected person likes apple juice is \( \frac{13}{30} \).
So the answer is D) 13/30.