There are two types of female honeybees: workers, which produce no eggs, and the queen, which produces eggs. Drone bees are males that are produced from the queen’s unfertilized eggs. A drone’s mother is the queen that laid the egg. But a drone has no father, because the egg was never fertilized. Worker females and queen females are produced from the queen’s fertilized eggs. So each type of female has a father as well as a mother, because the female eggs were fertilized. Describe how the numbers of ancestors of a drone honeybee are Fibonacci numbers.

A certain infectious disease of humans is caused by a virus. There are six main viral strains, and an individual can never be infected by the same strain twice. However, a second infection can occur by any of the other strains. The severity of the second infection depends on the identity of both the strain that caused the first infection and the strain causing the second infection, as well as the order in which these were acquired. How many different levels of severity are possible for an individual acquiring a second infection?levels of severity

A tire company wants to determine if tires made with a new type of tread will last longer than tires made with the original type of tread. The company decides to put tires with the new tread on 10 different vehicles and tires with the original tread on 10 different vehicles. "New” is written on one slip of paper and "Original” is written on another slip of paper. The two slips are placed in a bag and thoroughly mixed. A vehicle is selected and a slip is drawn. The corresponding tread of tires is assigned to the vehicle. The slip is put back into the bag and mixed. The next vehicle is selected and a slip is drawn. The corresponding tread is assigned to the vehicle. This procedure continues until all 20 vehicles have been assigned tires of the new or original types of tread. Does this procedure describe a completely randomized design for this experiment? Yes, the tires are randomly assigned to each vehicle. Yes, there are two treatments, new and original treads. No, even though…

Human blood may contain either or both of two antigens, A and B. Blood that contains only the A antigen is called type A, blood that contains only the B antigen is called type B, blood that contains both antigens is called type AB, and blood that contains neither antigen is called type O. At a certain blood bank, 35% of the blood donors have type A blood, 10% have type B, and 5% have type AB. (i) What is the probability that a randomly chosen blood donor is type O? (ii) A recipient with type A blood may safely receive blood from a donor whose blood does not contain the B antigen. What is the probability that a randomly chosen blood donor may donate to a recipient with type A blood? (b) A box contains 10 fuses. Eight of them are rated at 10 amperes (A) and the other two are rated at 15 A. Two fuses are selected at random. (i) What is the probability that the first fuse is rated at 15 A? (ii) What is the probability that the second fuse israted at 15 A, given that the first fuse is rated…

A game of “Doubles-Doubles” is played with two dice. Whenever a player rolls two dice and both die show the same number, the roll counts as a double.If a player rolls doubles, the player earns 5 points and gets another roll. If the player rolls doubles again, the player earns 5 more points. Whenever the player rolls the dice and does not roll a double, they lose points.How many points should the player lose for not rolling doubles in order to make this a fair game?   A) 5/6 B) 1 C) 5 D) 10/6

Some traits of plants and animals depend on inheritance of a single gene. This is called Mendelian inheritance, after Gregor Mendel (1822-1884). Each of us has an ABO blood type, which describes whether two characteristics called A and B are present. Every human being has two blood type alleles (gene forms), one inherited from our mother and one from our father. Each of these alleles can be A, B, or O. Which two we inherit determines our blood type. Here is a table that shows what our blood type is for each combination of two alleles.   Alleles inherited Blood type   A and A A A and B AB A and O A B and B B B and O B O and O O     We inherit each of a parent's two alleles with probability 0.5. We inherit independently from our mother and father. What is the probability that both children have different blood types?

C & J Realty has received 12 inquiries from prospective home buyers. In how many ways can the inquiries be directed to any three of the firm's real estate agents if each agent handles four inquiries?

A department store stocks three types of materials: A, B, and C.Each unit of type A occupies 0.2 square meters of shelf space, each unit of type B occupies 0.2 square meters of shelf space, and each unit of type C occupies 0.2 square meters of shelf space. The store has 100 square meters available for storage. Surveys show that the store should have on hand at least 18 units of material A and at least 22 units of A and B combined.Storage of one unit of brand A costs the store £19, brand B £9, and brand C £14. The store management wants to use all shelf space available and minimise the cost of storage. What is the minimum cost of storage that the store can achieve by choosing an optimal storage plan?

A co-rec team to play in an intramural tournament of indoor soccer should consist of three men and three women. There are five men and ten women to join that team. Within the fifteen people there is a husband and wife. In how many ways can that team be selected if it must contain either the wife or the husband but not both?

The Phony TV company makes two different types of television sets, OLED and LED, which are assembled by two different assembly lines. When Line One operates it assembles 30 units of the OLED model and 50 units of the LED model per hour. Line Two assembles 40 units of the OLED model and 40 units of the LED model per hour. Let x be the number of hours that Line One operates and y the number of hours Line Two operates. Phony needs to produce at least 3000 units of the OLED model and 4000 units of the LED model to fill an order. (a) Write down the inequalities that describe the assembly constraints. (b) Graph the feasible region determined by these constraints.