Questions: The accompanying table shows the numbers of male and female students in a certain region who received bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts (a) through (c) below. Click the icon to view the table. (a) The student is male or received a degree in the field The probability is (Type an integer or a decimal. Round to three decimal places as needed.) Table Degrees in Field Degrees Outside of Field Total Males 151,905 598,430 750,335 Females 114,713 832,531 947,244 Total 266,618 1,430,961 1,697,579

The accompanying table shows the numbers of male and female students in a certain region who received bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts (a) through (c) below.

Click the icon to view the table.
(a) The student is male or received a degree in the field

The probability is 

(Type an integer or a decimal. Round to three decimal places as needed.)

Table

  Degrees in Field  Degrees Outside of Field  Total 
 Males  151,905  598,430  750,335 
 Females  114,713  832,531  947,244 
 Total  266,618  1,430,961  1,697,579
Transcript text: The accompanying table shows the numbers of male and female students in a certain region who received bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts (a) through (c) below. Click the icon to view the table. (a) The student is male or received a degree in the field The probability is $\square$ (Type an integer or a decimal. Round to three decimal places as needed.) Table \begin{tabular}{|c|c|c|c|} \hline & Degrees in Field & Degrees Outside of Field & Total \\ \hline Males & 151,905 & 598,430 & 750,335 \\ \hline Females & 114,713 & 832,531 & 947,244 \\ \hline Total & 266,618 & 1,430,961 & 1,697,579 \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Identify the total number of students

The total number of students is given in the table as \( 1,697,579 \).

Step 2: Identify the number of male students

The number of male students is given in the table as \( 750,335 \).

Step 3: Identify the number of students who received a degree in the field

The number of students who received a degree in the field is given in the table as \( 266,618 \).

Step 4: Identify the number of male students who received a degree in the field

The number of male students who received a degree in the field is given in the table as \( 151,905 \).

Step 5: Calculate the probability of the student being male or receiving a degree in the field

Using the formula for the probability of \( A \) or \( B \): \[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \] where:

  • \( P(A) \) is the probability of the student being male.
  • \( P(B) \) is the probability of the student receiving a degree in the field.
  • \( P(A \text{ and } B) \) is the probability of the student being male and receiving a degree in the field.

Calculate each probability: \[ P(A) = \frac{750,335}{1,697,579} \] \[ P(B) = \frac{266,618}{1,697,579} \] \[ P(A \text{ and } B) = \frac{151,905}{1,697,579} \]

Now, plug these values into the formula: \[ P(A \text{ or } B) = \frac{750,335}{1,697,579} + \frac{266,618}{1,697,579} - \frac{151,905}{1,697,579} \]

Simplify the expression: \[ P(A \text{ or } B) = \frac{750,335 + 266,618 - 151,905}{1,697,579} = \frac{865,048}{1,697,579} \]

Step 6: Calculate the final probability

\[ P(A \text{ or } B) = \frac{865,048}{1,697,579} \approx 0.510 \]

The probability is \( 0.510 \) (rounded to three decimal places).

Final Answer

\(\boxed{0.510}\)

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