Damon likes heavy metal music, in fact, he loves it. Damon is therefore what we would call a metalhead. Damon likes the bar scene and enjoys talking to other metalheads when he goes out in the evening. Damon is also single, straight, and rather romantic, meaning he also likes to meet women when he goes out. Suppose that Damon is currently at a bar in which, not counting himself, 70.97% of the people in the bar are metalheads, 48.39% of the people are female, and 25.81% are both, to wit, female and metalhead. Suppose Damon starts talking to a random person.

1)What is the probability that this person be a female or a metalhead?

2)What is the probability that this person will be a female who is not a metalhead?

3)What is the probability that this person will be neither a female nor a metalhead?

4)What is the probability that this person is a metalhead, given that this person is female?

5)Are being a female and being a metalhead disjoint events? Prove or disprove with numbers!

6)Are being a female and being a metalhead independent events? Again, prove or disprove with numbers!