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.

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).