https://file.aiquickdraw.com/mathbot/file/172776374439984o6agn2.jpg

Let's go through the questions one by one based on the table provided.

### Table Summary:
- **Total Graduates** = 1000 (350 Male, 650 Female)
- **Confidence (Yes)** = 575 (225 Male, 350 Female)
- **No Confidence (No)** = 425 (125 Male, 300 Female)

### (i) A graduate is selected at random, find the probability that the graduate selected is:
#### 1. Confidence in getting a job
To find the probability that a randomly selected graduate has confidence in getting a job:
\[
P(\text{Confidence in getting a job}) = \frac{\text{Total graduates with confidence}}{\text{Total graduates}} = \frac{575}{1000} = 0.575
\]
So, the probability is **0.575**.

#### 2. Confidence in getting a job given that she is female
This is a conditional probability problem. We want to find \( P(\text{Confidence} | \text{Female}) \), which is the probability that a graduate has confidence given that the graduate is female.
\[
P(\text{Confidence} | \text{Female}) = \frac{\text{Number of females with confidence}}{\text{Total number of females}} = \frac{350}{650} = 0.538
\]
So, the probability is **0.538**.

### (ii) Are the events ‘No confidence in getting a job’ (N) and ‘Male’ (M) mutually exclusive? Justify your answer.
Two events are **mutually exclusive** if they cannot happen at the same time, i.e., their intersection is empty.

From the table:
- The number of males who have no confidence in getting a job is **125**.
- Since there are male graduates who have no confidence, these events are **not mutually exclusive**.

**Justification**: There are 125 males who have no confidence, so the two events \(N \cap M\) are not empty.

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Would you like more details or have any questions?

Here are 5 related questions:
1. What is the probability that a randomly selected graduate is female and has confidence in getting a job?
2. What is the probability that a randomly selected graduate is male and has no confidence in getting a job?
3. How would you calculate the probability that a randomly selected graduate is either male or has confidence in getting a job?
4. What does it mean for two events to be independent, and are the events "Confidence in getting a job" and "Male" independent?
5. What is the probability that a randomly selected male graduate has no confidence in getting a job?

**Tip**: When solving probability problems involving conditional probabilities, always remember to narrow the sample space to the condition being given (in this case, gender).

1000 randomly sampled graduates from ABC University were asked whether they had confidence in getting a job. A graduate is selected at random, find the probability that the graduate selected is: (1) confidence in getting a job, (2) confidence in getting a job given that she is female. Also, are the events 'No confidence in getting a job' (N) and 'Male' (M) mutually exclusive?

Solve probability problems related to confidence in getting a job for graduates, including finding the probability of a randomly selected graduate having confidence and conditional probabilities. Learn about mutually exclusive events with this detailed solution. Suitable for Grades 9-12.

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