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

Answer 1

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

1. Calculate the number of incorrect responses: \[ \text{Incorrect responses} = \text{Total responses} - \text{Correct responses} = 70 - 45 = 25 \]

2. The probability of an incorrect response is calculated by dividing the number of incorrect responses by the total number of responses: \[ P(\text{incorrect}) = \frac{\text{Number of incorrect responses}}{\text{Total responses}} = \frac{25}{70} \]

3. Now simplify the fraction \(\frac{25}{70}\):

   • The greatest common divisor (GCD) of 25 and 70 is 5.
   • Divide both the numerator and the denominator by 5: \[ \frac{25 \div 5}{70 \div 5} = \frac{5}{14} \]

Therefore, the empirical probability of David's incorrect responses is \(\frac{5}{14}\).