answer this questions in detail

1) A sample of four electronic components is taken from the output of a production line. The probabilities of the various outcomes are calculated to be: E}; [0 defectives] = l0.6561, R; [l defective] = 0.2916, 3;: [2 defectives] = 0.0486, R; [3 defectives] = 0.0036, R; [4 defectives] = 0.0001. What is the probability of at least one defective? 2) A card is drawn from a deck of 52 playing cards, what is the probability that the card is a queen or a heart? 3) The class registrations of 120 students are analyzed. It is found that 30 of the students do not take any of Applied Mechanics, Chemistry, or Computers.15 of them take only Applied Mechanics. 25 of them take Chemistry and Computers but not Applied Mechanics. 20 of them take Applied Mechanics and Computers but not Chemistry. 10 of them take all three of Applied Mechanics, Chemistry, and Computers. A total of 45 of them take Chemistry. 5 of them take only Chemistry. a) How many of the students take Applied Mechanics and Chemistry but not Computers? b) How many of the students take only Computers? c) What is the total number of students taking Computers? d) If a student is chosen at random from those who take neither Chemistry nor Computers, what is the probability that he or she does not take Applied Mechanics either? e) If one of the students who take at least two of the three courses is chosen at random, what is the probability that he or she takes all three courses? 4) Four of the light bulbs in a box of ten bulbs are burnt out or otherwise defective. If two bulbs are selected at random without replacement and tested, (i) what is the probability that exactly one defective bulb is found? (ii) What is the probability that exactly two defective bulbs are found