(a) A group of financial analysts researches the changes in share prices for Public Limited Companies (PLCs) during a three year period. A share prices increase of more than 5% is called a significant share price rise. The financial analysts notice that if a company has a significant share price rise they are more likely to replace their CEO during the three year period. The probability that company's share price has a significant rise is 6%. If a company has a significant share price rise, the probability that they will replace their CEO is found to be 55%. Out of the companies that do not have a significant share price rise, only 30% will replace their CEO. (i) Draw a probability tree, showing all probabilities, to represent this situation and find the probability that a company will replace their CEO during the three year time period. (ii) Find the probability that a company who replaced their CEO had a significant share price rise. State any theorems you use, using probability symbols.
