In a sample study of 642 people, it was found that 514 people have a high school certificate. If a person is selected at random, the probability that the person do not have a high school certificate is

Options

A. `251//321`
B. `253//321`
C. `251//329`
D. `64//321`

Answer

To find the probability that a randomly selected person does not have a high school certificate, we can follow these steps:

### Step 1: Identify the total number of people surveyed.
The total number of people surveyed is given as 642.

### Step 2: Identify the number of people who have a high school certificate.
According to the problem, 514 people have a high school certificate.

### Step 3: Calculate the number of people who do not have a high school certificate.
To find the number of people who do not have a high school certificate, we subtract the number of people who have a certificate from the total number of people surveyed:
\[ \text{Number of people without a high school certificate} = \text{Total people} - \text{People with a certificate} \]
\[ = 642 - 514 = 128 \]

### Step 4: Use the probability formula.
The probability \( P \) of an event is given by the formula:
\[ P(\text{not having a high school certificate}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
In this case, the number of favorable outcomes is the number of people who do not have a high school certificate (128), and the total outcomes is the total number of people surveyed (642):
\[ P(\text{not having a high school certificate}) = \frac{128}{642} \]

### Step 5: Simplify the fraction.
To simplify \( \frac{128}{642} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 128 and 642 is 2:
\[ \frac{128 \div 2}{642 \div 2} = \frac{64}{321} \]

### Final Answer:
The probability that a randomly selected person does not have a high school certificate is:
\[ \frac{64}{321} \]

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