3. (12 points) A "buddy tree" grows in the following way: . It starts as a single exposed bud. . Each week, all the exposed buds either flower or branch into two new exposed buds. The probability that an exposed bud will flower is 5/8. The probability that an exposed bud will branch is 3/8. 3/8 5/8 . If the bud branches, then it splits into two branches each with a single exposed bud at the end. A mature tree is a tree that does not have any exposed buds. A mature tree does not grow any more. A scrub is a mature tree that never branches. A scrub is a mature tree with only one flower. Here is an example of a mature tree that is not a scrub:Here is an example of a mature tree that is not a scrub: Here is an example of a mature tree that is a scrub: (a) (4 points) If you plant one tree (starting as a single bud), what is the probability that it will fully mature in 2 weeks or less.(b) (4 points) What is the expected total number of flowers of a single mature tree? (c) (4 points) If you plant n trees, after all of them have matured, what is the expected number of flowers that are not scrubs