An analyst attempts to predict total sales next year. He believes that, if the average growth rate of customers in the next year is greater than 10%, the probability of significant growth in total sales is 0.2. If the average growth rate of customers in next year is lower than 5%, the probability of significant growth in total sales is estimated to be 0.8. Finally, if the average growth rate of customers in the next year is between 5% and 10%, the probability of significant growth in total sales is put at 0.2. The analyst estimates that the probability is 0.5 that the rate next year will be greater than 10% and 0.2 that it will be lower than 5%.

a.What is the estimated probability that the average growth rate of customers in next year is no lower than 5%?

b.What is the estimated probability that the average growth rate of customers will be greater than 10% and significant growth in total sales will realize next year?

c.What is the estimated probability that the average growth rate of customers will be no lower than 5% and significant earnings growth will realize next year?

d.What is the probability that this corporation will experience significant growth in total sales next year?

e.Suppose that the corporation exhibits significant growth in total sales next year. Given this observation, what is the conditional probability that the average growth rate of customers has been greater than 10%?

f.What is the conditional probability that this corporation will experience significant growth in total sales given that the average growth rate of customers is no lower than 5%?