Question

the questions on a test consist of 1 multiple choice, 2 essays, and 10 free responses. if the questions are ordered randomly, what is the probability that the first question is a free response? give your answer as a simplified fraction. provide your answer below.

Explanation:

Step1: Calculate total number of questions

We have 1 multiple - choice, 2 essays, and 10 free - response questions. The total number of questions \(n = 1+2 + 10=13\).

Step2: Calculate number of free - response questions

The number of free - response questions \(m = 10\).

Step3: Calculate the probability

The probability \(P\) that the first question is a free - response is given by the formula \(P=\frac{\text{Number of free - response questions}}{\text{Total number of questions}}\). So \(P=\frac{10}{13}\).

Answer:

\(\frac{10}{13}\)