probability

e :1 workers. nd out how 1e cars in which they were he average of the n values. :n cars in the lot. nd out how a in those cars. and take the 'alues. inary deck of 52 cards is shuf- re then turned over one at a e appears. Given that the rst to appear1 what is the condi- it the card following it is the :Ialls in a box. of which 9 have used. Three of the balls are ayed with. and then returned mother 3 balls are randomly 1):. Find the probability that as ever been used. one containing 1 black and 1 her 2 black and 1 white mar- d at random. and a marble is [dom. What is the probability lack? What is the probability [5 the one selected given that sad a biopsy on a possibly can- anting to spoil a weekend fam- ot want to hear any bad news . But if she tells the doctor to s good. then if the doctor does can conclude that the news is 31\" of probability. les. Aquina to ip a coin. If it comes up to call if the news is good and is bad. If the coin comes up ot to call. In this way. even if ill. the news is not necessarily .bability that the tumor is can- onditional probability that the given that the doctor does not e larger. or or ,3'.' of e. and prove your answer 'en with probability p}. where pg, = .35.p4 : .3. A child randomly chosen. Given that st child in the family. nd the ity that the family has 3.33. 3.34. 3.35. 3.36. 3.31 3.38. 3.3!}. 3.4!}. On rainy days. Joe is late to work with probability .3; on nonrainy days. he is late with probability .1. With probability .1". it will rain tomorrow. {11] Find the probability that Joe is early tomor- row. {Ii} Given that Joe was early. what is the condi- tional probability that it rained'lI In Example 3f. suppose that the new evidence is subject to different possible interpretations and in fact shows only that it is 9t] percent likely that the criminal possesses the characteristic in question. In this case. how likely would it be that the suspect is guilty (assuming. as before. that he has the charac- teristic)? With probability .fi. the present was hidden by mom: with probability .4. it was hidden by dad. When mom hides the present. she hides it upstairs TI} percent of the time and downstairs 3D percent of the time. Dad is equally likely to hide it upstairs or downstairs. {a} What is the probability that the present is upstairs? [b] Given that it is downstairs. what is the proba- bility it was hidden by dad? Stores A. B. and C have 5t}. T5. and 1m employees. respectively. and 5D. t}. and TL} percent of them respectively are women. Resignations are equally likely among all employees. regardless of sex. One woman employee resigns. What is the probability that she works in store C\"? {a} A gambler has a fair coin and a two-headed coin in his pocket. He selects one of the coins at random; when he ips it. it shows heads. What is the probability that it is the fair coin? [b] Suppose that he ips the same coin a second time and. again. it shows heads. Now what is the probability that it is the fair coin?I {c} Suppose that he ips the same coin a third time and it shows tails. Now what is the prob- ability that it is the fair coin? Urn A has 5 white and '3' black balls. Urn E has 3 white and 12 black balls. We ip a fair coin. If the outcome is heads. then a ball from urn A is selected. whereas if the outcome is tails. then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails'lI In Example 3a. what is the probability that some- one has an accident in the second year given that he or she had no accidents in the rst year? Consider a sample of size 3 drawn in the following manner: We start with an urn containing 5 white