Even though Recycle operates a successful business in Sydney. In recent years it has been looking for opportunities to expand its business in other parts of Australia. Anna, one of the managing directors, was approached by GreenTech Ltd, a company that is currently building a commercial recycling plant in Western Australia, and just announced a new partnership with a famous chocolate manufacturer, using a process that turns old polypropylene into clean material. The standard recycling process grinds up colored plastic to create a dull grey or black material that does not look attractive. GreenTech’s new technology melts down plastic and then uses a gas solvent and filtration to separate out dyes, odors, and other contaminants, resulting in a clear material that looks like new plastic. Unlike some other new recycling tech, it doesn’t use chemical reactions. GreenTech approached Anna with the proposal that Recycle would purchase their new technology. Anna mentioned this to the board members at a board meeting and the board members were enthusiastic on the grounds that the technology might be beneficial for their business to grow and be more profitable. However, Anna informed GreenTech that Recycle could not be involved because the technology was too expensive. Instead, she told GreenTech that she would personally approach other recycling companies throughout Australia to purchase the technology and, if successful, she would like to be paid 10% of the sale price. However, Anna formed a joint venture company with GreenTech – ABC Pty Ltd, and the venture proved a great financial success. Later, when some members of the Smith family queried about her previous proposal with GreenTech, Anna did not disclose anything to Recycle or the Smith family. The new technology can recycle 119 million pounds of polypropylene, creating demand for nearby recyclers to begin to separate out materials. The product the technology helped to produce is already in such high demand that it has been pre-sold for the next 20 years. Big multinational corporations, which have a goal to make all their packaging recyclable or reusable by 2025, and which also aim to increase the recycled content in their packaging, announced that it was partnering with ABC Pty Ltd to help meet their goals. ABC Pty Ltd also aims to quickly scale up with plans to build 10 recycling plants in Australia.

Please advise Recycle Pty Ltd and the ASIC if any of its directors have breached their duties. Discuss by citing relevant Australian laws.

The familial aggregation of respiratory disease is a well-established clinical phenomenon. However, whether this aggregation is due to genetic or environmental factors or both is somewhat controversial. An investigator wishes to study a particular environmental factor, namely the relationship of cigarette-smoking habits in the parents to the presence or absence of asthma in their oldest child age 5 to 9 years living in the household (referred to below as their offspring). Suppose the investigator finds that (1) if both the mother and father are current smokers, then the probability of their offspring having asthma is 0.15; (2) if the mother is a current smoker and the father is not, then the probability of their offspring having asthma is 0.13; (3) if the father is a current smoker and the mother is not, then the probability of their offspring having asthma is 0.05; and (4) if neither parent is a current smoker, then the probability of their offspring having asthma is 0.04. 1. (5 points) Suppose the smoking habits of the parents are independent and the probability that the mother is a current smoker is 0.4, whereas the probability that the father is a current smoker is 0.5. What is the probability that both the father and mother are current smokers? 2. (3 points) Consider the subgroup of families in which the mother is not a current smoker. What is the probability that the father is a current smoker among such families? How does this probability differ from that calculated in Problem 1? 3. Suppose, alternatively, that if the father is a current smoker, then the probability that the mother is a current smoker is 0.6; whereas if the father is not a current smoker, then the probability that the mother is a current smoker is 0.2. Also assume that statements 1, 2, 3, and 4 above hold. 4. (9 points) If the probability that the father is a current smoker is 0.5, what is the probability that the father is a current smoker and that the mother is not a current smoker? 5. (3 points) Are the current smoking habits of the father and mother independent? Why or why not? 6. (22 points) Under the assumptions made in Problem 3 and 4, find the unconditional probability that the offspring will have asthma.