SURE Document1 - Word Sign in 0 - 0 x Share File Home Insert Design Layout References Mailings Review View Help Tell me what you want to do Question 1 (a) Many researchers have developed models based on financial ratios that predict whether or not a company will go bankrupt in the next year. In a test of one such model, the model correctly predicted iii. Find the probability that wife invests in medium to high risk fund. [4 marks) iv. Given that the wife invests in medium to high risk fund, find the probability that the husband also invests in them. [4 marks] bankruptcy for 85% of firms if they in fact did fail and it correctly predicted non-bankruptcy for 82% of firms given that they did not fail. Suppose that the model maintains the same reliability when applied to a new group of 100 firms, of which four fail in the year following the time at which the model makes its predictions. (0) () Define the related variables and draw tree diagram for the above scenario. Find the probability that the model's prediction will prove to be correct. (iii) Find the probability that the model makes an incorrect prediction. (iv) Find the probability that one of these firms will fail, given that the model has predicted it will go bankrupt. v) Find the probability that one of these firms will not fail, given that the model has predicted it will go bankrupt. (b) Your favorite team is in the final playoffs. You have assigned a probability of 60% that it will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 70% of the time. When they lose the series, they win the first game 25% of the time. The first game is over, your team has lost. 1. Define the related variables and draw tree diagram for the above scenario. ii. What is the probability that it will win the series? Ans: 0.375 (c)A financial company is studying investment choices for husbands and wives from two income families. Based on previous experience, it was found that 70% of the husbands invest in medium to high risk bonds. When the husbands invest in medium to high risk bonds, 50% of wives also invest in them. When the husbands invest in low risk funds, 80% of the wives also invest in them, while the rest invests in medium to high risk bonds. 1. Define the events involved for the above scenario. Draw a tree diagram and its probabilities of investment choices for husbands and wives. [8 marks] it. Find the probability that both husband and wife invest in medium to high funds. [3 marks] Page 2 of 2 428 words DX -- - + 72% 7:07 AM Type here to search o Bi e a H = p = x N 9 w 3/7/2020 W SURE Document1 - Word Sign in 0 - 0 x Share File Home Insert Design Layout References Mailings Review View Help Tell me what you want to do Question 1 (a) Many researchers have developed models based on financial ratios that predict whether or not a company will go bankrupt in the next year. In a test of one such model, the model correctly predicted iii. Find the probability that wife invests in medium to high risk fund. [4 marks) iv. Given that the wife invests in medium to high risk fund, find the probability that the husband also invests in them. [4 marks] bankruptcy for 85% of firms if they in fact did fail and it correctly predicted non-bankruptcy for 82% of firms given that they did not fail. Suppose that the model maintains the same reliability when applied to a new group of 100 firms, of which four fail in the year following the time at which the model makes its predictions. (0) () Define the related variables and draw tree diagram for the above scenario. Find the probability that the model's prediction will prove to be correct. (iii) Find the probability that the model makes an incorrect prediction. (iv) Find the probability that one of these firms will fail, given that the model has predicted it will go bankrupt. v) Find the probability that one of these firms will not fail, given that the model has predicted it will go bankrupt. (b) Your favorite team is in the final playoffs. You have assigned a probability of 60% that it will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 70% of the time. When they lose the series, they win the first game 25% of the time. The first game is over, your team has lost. 1. Define the related variables and draw tree diagram for the above scenario. ii. What is the probability that it will win the series? Ans: 0.375 (c)A financial company is studying investment choices for husbands and wives from two income families. Based on previous experience, it was found that 70% of the husbands invest in medium to high risk bonds. When the husbands invest in medium to high risk bonds, 50% of wives also invest in them. When the husbands invest in low risk funds, 80% of the wives also invest in them, while the rest invests in medium to high risk bonds. 1. Define the events involved for the above scenario. Draw a tree diagram and its probabilities of investment choices for husbands and wives. [8 marks] it. Find the probability that both husband and wife invest in medium to high funds. [3 marks] Page 2 of 2 428 words DX -- - + 72% 7:07 AM Type here to search o Bi e a H = p = x N 9 w 3/7/2020 W
