https://file.aiquickdraw.com/mathbot/file/17263485272032qxfis6z.jpg

Let's break down the questions in the image and solve them step by step.

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### **Question 1**: 
A lottery game has balls numbered 1 through 15. A randomly selected ball has an even number or a 6.  
We need to find the probability of this event.

**Step 1**: Identify the numbers.  
- The even numbers between 1 and 15 are: 2, 4, 6, 8, 10, 12, 14.  
- Notice that 6 is both an even number and listed as a condition in the problem, so we don't double count it.

**Step 2**: Count the favorable outcomes.  
- The favorable outcomes are the even numbers: 2, 4, 6, 8, 10, 12, 14. So there are 7 favorable outcomes.

**Step 3**: Find the total number of outcomes.  
- The total number of balls is 15 (numbered 1 through 15).

**Step 4**: Compute the probability.
\[
P(\text{even number or 6}) = \frac{7}{15}
\]

The correct answer is **B) \(\frac{7}{15}\)**.

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### **Question 2**:
The probability that a student at a certain college is male is 0.45. The probability that a student has a job off campus is 0.33. The probability that a student is male and has a job off campus is 0.15. Find the probability that a student chosen at random is male or has an off-campus job.

**Step 1**: Use the formula for the union of two events:
\[
P(\text{Male or Job}) = P(\text{Male}) + P(\text{Job}) - P(\text{Male and Job})
\]
Where:
- \( P(\text{Male}) = 0.45 \)
- \( P(\text{Job}) = 0.33 \)
- \( P(\text{Male and Job}) = 0.15 \)

**Step 2**: Substitute values into the formula:
\[
P(\text{Male or Job}) = 0.45 + 0.33 - 0.15 = 0.63
\]

The correct answer is **A) 0.63**.

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Would you like more detailed explanations or have any questions about these problems? Here are 5 related questions you might want to consider:

1. What is the probability of selecting an odd-numbered ball from the same lottery game?
2. If the lottery balls are numbered 1 through 20, how does the probability change for selecting an even number or a 6?
3. What if the probability that a student is female and has a job off campus is given, how would that change the outcome in Question 2?
4. How would you calculate the probability that a student is neither male nor has an off-campus job in Question 2?
5. If there are 10 male students with jobs off campus and 30 students in total, how would you find the actual number of students with jobs off campus?

**Tip**: Always check if events overlap (like "male" and "job") to avoid double-counting in probability problems.

A lottery game has balls numbered 1 through 15. A randomly selected ball has an even number or a 6.
The probability that a student at a certain college is male is 0.45. The probability that a student at that college has a job off campus is 0.33. The probability that a student is male and has a job off campus is 0.15. If a student is chosen at random from the college, what is the probability that the student is male or has an off-campus job?

Learn how to calculate the probability of drawing an even-numbered ball from a set of 15 or determining the likelihood that a student is male or has an off-campus job at a college. Includes step-by-step solutions for each problem, focusing on probability concepts and set theory. Suitable for students in Grades 10-12.

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