On a science quiz, David got 45 out of 70 items correct. What is the empirical probability of his incorrect responses? Write your answer in the simplest form of a fraction.(1 point)

1 answer

To find the empirical probability of David's incorrect responses, we first need to determine how many items he got incorrect.

David answered 45 questions correctly out of 70 total questions. Therefore, the number of incorrect responses is:

\[ 70 - 45 = 25 \]

Now, to find the empirical probability of getting an incorrect response, we use the formula for probability:

\[ P(\text{incorrect}) = \frac{\text{Number of incorrect responses}}{\text{Total number of responses}} \]

Substituting the values we have:

\[ P(\text{incorrect}) = \frac{25}{70} \]

Next, we simplify the fraction \( \frac{25}{70} \). Both the numerator and the denominator can be divided by 5:

\[ \frac{25 \div 5}{70 \div 5} = \frac{5}{14} \]

Thus, the empirical probability of David's incorrect responses, in simplest form, is:

\[ \boxed{\frac{5}{14}} \]