Questions: test consist of 10 multiple choices, 3 essays and 9 free responses. If the questions are ordered randomluy, What is the probability that the first gouestion is a free response?

test consist of 10 multiple choices, 3 essays and 9 free responses. If the questions are ordered randomluy, What is the probability that the first gouestion is a free response?
Transcript text: test consist of 10 multiple choices, 3 essays and 9 free responses. If the questions are ordered randomluy, What is the probability that the first gouestion is a free response?
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Solution

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Solution Steps

Step 1: Determine Total Questions

The total number of questions in the test is calculated by summing the different types of questions: \[ \text{Total Questions} = 10 \, (\text{multiple choices}) + 3 \, (\text{essays}) + 9 \, (\text{free responses}) = 22 \]

Step 2: Identify Free Response Questions

The number of free response questions is given as: \[ \text{Free Response Questions} = 9 \]

Step 3: Calculate Probability

The probability that the first question is a free response question is given by the ratio of the number of free response questions to the total number of questions: \[ P(\text{First Question is Free Response}) = \frac{\text{Free Response Questions}}{\text{Total Questions}} = \frac{9}{22} \approx 0.4091 \]

Final Answer

The probability that the first question is a free response is approximately \\(\boxed{0.4091}\\).

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