A brilliant young golfer wins 15% of the tournaments she enters. We will assume the results of each tournament are independent of other tournaments. a) If she enters 20 tournaments this year, what is the probability she will win none of them? b) What is the expected value of the number of tournaments she must enter in order to win her  first tournament? What is the variance of that number?

29 percent of all Samsung cell phones are submitted for service while under warranty. Of these, 66 percent can be repaired, whereas the other 34 percent must be replaced with new units. If a company purchases 12 Samsung cell phones, what is the probability that exactly 2 will end up being replaced under warranty? What would the mean number of cell phones being replaced under warranty be? What would be the variance be for the cell phones being replaced by warranty?.

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 52 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If one shipment of 4000 aspirin tablets actually has a 5​% rate of​ defects, what is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?   The probability that this whole shipment will be accepted is ______ ​(Round to four decimal places as​ needed.)   The company will accept ____% of the shipments and will reject ____% of the​ shipments, so______________ (many of the shipments will be rejected or almost all of the shipments will be accepted. ​(Round to two decimal places as​ needed.)

All human blood can be "ABO-typed" as one of O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen person in a country. Blood type A National probability 0.43 0.12 AB ? (a) What is the national probability of type AB blood? O 0.41 (b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly chosen person from this country can donate blood to Maria?