A survey taken by 150 people revealed that 65 like apple juice while 85 dislike it. One person is randomly chosen from this group. What is the chance that the chosen person dislikes apple juice? Write your answer as a ratio in simplest form.(1 point)

Responses

65/150
Start Fraction 65 over 150 End Fraction

13/30
Start Fraction 13 over 30 End Fraction

13/17
Start Fraction 13 over 17 End Fraction

17/30

1 answer

To determine the probability that a randomly chosen person dislikes apple juice, we first note the total number of people surveyed and how many of them dislike apple juice.

  1. The total number of people surveyed is 150.
  2. The number of people who dislike apple juice is 85.

The probability \( P \) that a randomly chosen person dislikes apple juice can be calculated using the formula:

\[ P(\text{dislikes apple juice}) = \frac{\text{Number of people who dislike apple juice}}{\text{Total number of people surveyed}} = \frac{85}{150} \]

Next, we need to simplify the fraction \( \frac{85}{150} \).

First, we find the greatest common divisor (GCD) of 85 and 150. The prime factorization of 85 is \( 5 \times 17 \), and for 150, it is \( 2 \times 3 \times 5^2 \). The common factor is 5.

Now, we divide the numerator and the denominator by their GCD:

\[ \frac{85 \div 5}{150 \div 5} = \frac{17}{30} \]

Thus, the probability that the chosen person dislikes apple juice is \( \frac{17}{30} \).

Therefore, the answer is:

\[ \text{17/30} \]

This corresponds to the option:

17/30