Exercise 2 2.1 The probability that a gunning athlete hits the target is 0.45, X means the total amount that he has already shot when he hits the target for the first time. Write the probability distribution of X, and evaluate the probability that X take on even number. 2.2 The probability that a basketball athlete hits the rim of basketball is 0.9. Evaluate the probability distribution of the number of hitting times X if he shoots the basket twice in- dependently. 2.3 A child plays a round of crazy golf. The round of golf consists of 9 holes. The number of shots the child takes at each hole is geometrically distributed with success probability 0.25. (1) Calculate the probability that the child gets a 'hole in one' on the first hole (a hole in one means the child only takes one shot on that hole). (2) Calculate the probability that the child gets at least one 'hole in one' during their round of golf. (3) Calculate the probability that the child takes 36 shots in completing his round of golf. 2.4 In a batch of ten light bulbs four are defective. How many different ways are there to select a sample space of size 3? According to your first way, find the probability that in such a sample: Probability and statistics .36. 2.11 A doctor has 5 patients with migraine headaches. He prescribes for all five patients a drug that relieves the headaches of 0.82 of such patients. What is the probability that the medicine will not relieve the headaches of these two patients? 2.12 Let X denote the total number insects on a leaf and suppose that X ~ p(x; 1 = 3). (1) What is the probability that there are no insects on the leaf? (2) What is the probability that there are 4 insects on the leaf? (3) What is the probability that in a random sample of 8 leaves, just one leaf has no insects on it