answer this questions in details

1) Suppose 30% of the girls in a class received an A in the test and 25% of the boys received anA. The class is 60% girls. Given that a student selected at random received an A, what is the probability that the student selected is a girl? 2) Suppose a factory has machines A, B and C that produce screws. The factory's record shows that Machine A, B and C produce, respectively 2%. 1% and 3% defective screws. Out of the total production, machines A, B and C produce, respectively 35% , 25% and 40% of all screws. A screw is selected at random from the factory. a) What is the probability that the screw selected is defective? b) Given that the screw is defective, what is the probability that it was produced by machine C? 3) An urn contains 15 red and 12 green balls. Two successive drawings of 6 balls are made such that i) balls are replaced before the second draw ii) balls are not replaced before the second draw. Find the probability that the rst drawing will give 6 red and the second 6 green balls. 4) The number of meteors found by a radar system in any 30-second interval under specied conditions averages 1.65. Assume the meteors appear randomly and inde- pendently. a) What is the probability that no meteors are found in a one-minute interval? b) What is the probability of observing at least four but not more than seven meteors in two minutes of observation? 5) In the long run 3 vessels out of every 100 are sunk. If 10 vessels are out, what is the probability that i) Exactly 6 will arrive safely ii) At least 6 will arrive safely? 6) A random variable X has the following probability distribution: Values 0 1 2 3 4 5 6 7 8 ofX, x P(x) a 3a 5a 7a 9a lla 13a 15a 17a i) Determine the value of :1. ii) Find P(X 0.5? and iv) Find out the distribution function of X