if it's possible please show all the steps and type the answer. Thank you

1) A group of college DJs surveyed students to find out what music to plan for their upcoming parties. 30% of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. 15% of the respondents selected both dubstep and trance.

(a) What's the proportion of students that like neither trance music nor dubstep?

(b) What's the proportion of students that didn't select any of the music options (dubstep, trance, house) available on the survey?

2) In a lottery, players choose one number from the range 1 to 80; 20 winning numbers are displayed on a screen every four minutes. If you choose just one number, your probability of winning is 20/80, or 0.25. Lester plays one number eight times as he sits in a bar. What is the probability that all eight bets lose?

3) A desk lamp produced by The Luminar Company was found to be defective. There are three factories (A, B, C) where such desk lamps are manufactured. A Quality Control Manager (QCM) is responsible for investigating the source of found defects. The QCM knows the following about the company's desk lamp production and the possible source of defects: Factory A produces 35% of total production and 1.5% of their lamps are defective. Factory B produces 35% of total production and 1% of their lamps are defective. Factory C produces 30% of total production and 2% of their lamps are defective.

(a) What is the probability that a randomly selected lamp is defective?

(b) If a randomly selected lamp is defective, what is the probability that the lamp was manufactured in factory C?

4- I roll a fair die twice and obtain two numbers X1 = result of the first roll, and X2 = result of the second roll.

(a) Find P(X1 < X2)

(b) Find the probability that " you observe a 3 or 6 at least once".