Question
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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. Pift Click the icon to view the table. 0 of 1 (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.)

Ask by Todd Carroll. in the United States
Feb 27,2025

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Tutor-Verified Answer

Answer

The probability is 1.000.

Solution

To find the probability of the event described in part (a), we need to follow these steps: 1. **Extract the known conditions**: We need the total number of male and female students who received bachelor's degrees in the specified field. This information is typically found in the accompanying table. 2. **Calculate the total number of students**: This is the sum of male and female students. 3. **Identify the event**: The event is that a student is either male or received a degree in the field. Since all students in the table received a degree in the field, the probability of selecting a student who is male or received a degree in the field is essentially the probability of selecting any student. 4. **Calculate the probability**: The probability \( P \) of an event is given by the formula: \[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] Since we don't have the actual numbers from the table, let's denote: - \( M \) = number of male students - \( F \) = number of female students The total number of students \( T \) is: \[ T = M + F \] The probability of selecting a student who is male or received a degree in the field is: \[ P(\text{male or received a degree}) = \frac{M + F}{T} = \frac{T}{T} = 1 \] Now, if you provide the actual numbers from the table, I can calculate the specific probability for you.

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The Deep Dive

To tackle this problem, we would need the specific numbers of male and female students who received degrees in that particular field, which you've referred to in a table. However, I can guide you on how to calculate probabilities involving events like this! When calculating the probability of either event happening (in this case, being male or receiving a degree in the field), you add the probabilities of each event and subtract the probability of both occurring, as you don’t want to double-count that section. The formula looks like this: P(Male or Degree) = P(Male) + P(Degree) - P(Male and Degree). This will give you the probability you're looking for! Now, onto common pitfalls: Remember to check if the numbers you're working with include all students in that region! If you’re missing any, your total will be skewed, affecting your probabilities. Also, don't forget to round your answer correctly to three decimal places!

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